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On a generalization of the Reidemeister spectrum of a finite group, submitted.

Isolated subgroups of ZM-groups, submitted.

A generalization of sequenceable groups, submitted.

A generalization of the Chermak-Delgado measure of a finite group, submitted.

On the number of edges of cyclic subgroup graphs of finite groups II, submitted.

Finite groups whose subgroup graphs are regular (with G. Fasolă), submitted.

PSOS-groups revisited, accepted for publication in Int. Electron. J. Algebra.

On a divisibility condition related to the sum of element orders of a finite group, accepted for publication in Asian-Eur. J. Math.

Two new functions related to the sum of element orders of a finite group, accepted for publication in J. Algebra Appl., cited by:

M.K. Singh, Odd square roots and the sum of element orders on S_n and A_n, 2026.

A note on the number of edges of cyclic subgroup graphs, accepted for publication in Sci. Stud. Res., Ser. Math. Inform.

On a function related to the Chermak-Delgado measure of a finite group, accepted for publication in Facta Univ., Ser. Math. Inform., cited by:

A.K. Asboei, Boundary cases and central extensions for the normalized Chermak-Delgado measure, 2026.

A note on finite groups with few conjugacy classes of subgroups, accepted for publication in Comm. Algebra.

A criterion for solvability of a finite group by the harmonic mean of element orders (with I.C. Pleşca), accepted for publication in Beitr. Algebra Geom.

Minimal (just) non-sequenceable groups (with I.C. Pleşca), accepted for publication in Bull. Univ. "Transilvania" Braşov, ser. III.

On the number of conjugacy classes of subgroups of a finite group (with M.S. Lazorec), Mediterranean J. Math., vol. 23 (2026), no. 6, article ID 184 (pdf), cited by:

M.S. Lazorec, Detecting solvability, supersolvability and CLT properties via an invariant based on conjugacy classes of subgroups, 2026.

The Reidemeister spectrum of ZM-groups, Bull. Aust. Math. Soc., vol. 114 (2026), no. 1, 101-106 (pdf).

Counting conjugacy classes and automorphism-conjugacy classes of ZM-groups, Asian-Eur. J. Math., vol. 19 (2026), no. 9, article ID 2550144, ZBL 08203352 (pdf).

A remark on the number of automorphisms of finite abelian groups, Elem. Math., vol. 81 (2026), no. 1, 26-28 (pdf), cited by:

R. Molinier, A remark on the number of automorphisms of some algebraic structures, 2025.

R. McCulloch, An answer regarding automorphisms of finite abelian groups, 2026.

S. Sureaux, Automorphism ratios of finite groups, 2026.

Corrigendum and addendum to "Finite groups with integer harmonic mean of element orders" (with I.C. Pleşca), J. Algebra Appl., vol. 25 (2026), no. 6, article ID 2691001, MR 5021818, ZBL 08155796 (pdf).

Finite groups with dense CD-subgroups (with R. McCulloch), Int. J. Group Theory, vol. 15 (2026), no. 2, 49-53, MR 4997849, ZBL 08157593 (pdf), cited by:

R. McCulloch, Groups with dense Chermak-Delgado subgroups, The 2025 Zassenhaus Group Theory and Friends Conference, USA, 2025.

F. Aseeri, J. Kaspczyk, Finite groups with dense ICO-subgroups, 2026.

Perfect totient groups, Sci. Stud. Res., Ser. Math. Inform., vol. 35 (2025), no. 2, 65-70 (pdf).

Finite groups with dense solitary subgroups, Bull. Korean Math. Soc., vol. 62 (2025), no. 5, 1391-1395, MR 4965768, ZBL 08143636 (pdf), cited by:

F. Aseeri, J. Kaspczyk, Finite groups with dense ICO-subgroups, 2026.

Finite groups with many normalizers, Czech. Math. J., vol. 75 (2025), no. 3, 767-772, MR 4961339, ZBL 08127780 (pdf), cited by:

F. Aseeri, J. Kaspczyk, Finite groups with dense ICO-subgroups, 2026.

Almost and quasi Leinster groups (with I.C. Pleşca), Sci. An. Univ. "Ovidius" Constanţa, ser. Math., vol. XXXIII (2025), fasc. 3, 121-134, MR 4982917 (pdf).

A result on certain sums of element orders in finite groups, Results Math., vol. 80 (2025), no. 4, article ID 111, MR 4907670, ZBL 1569.20050 (pdf).

Almost abelian numbers (with I.C. Pleşca), Bull. Aust. Math. Soc., vol. 111 (2025), no. 3, 518-523, MR 4903218, ZBL 08061416 (pdf), cited by:

M.S. Lazorec, On two problems about order sequences of finite groups, J. Algebraic Combin., vol. 62 (2025), no. 2, article ID 29.

A result on the Chermak-Delgado measure of a finite group, Facta Univ., Ser. Math. Inform., vol. 40 (2025), no. 1, 45-48, MR 4913420, ZBL 08045811 (pdf).

Finite groups whose subgroup graph contains a vertex of large degree, Arch. Math., vol. 124 (2025), no. 5, 475-484, MR 4891756, ZBL 08028315 (pdf).

Finite groups with integer harmonic mean of element orders (with I.C. Pleşca), J. Algebra Appl., vol. 24 (2025), no. 3, article ID 2550083, MR 4853121, ZBL 1556.20044 (pdf), cited by:

I.C. Pleşca, Number theory concepts in group theory, Proceedings of The Tenth Congress of Romanian Mathematicians, Piteşti, Romania, 2023.

A characterization of A_5 by its average order, Int. J. Group Theory, vol. 14 (2025), no. 3, 117-123, MR 4822892, ZBL 1553.20067 (pdf), cited by:

B. Taeri, Z. Tooshmalani, Minimal non-abelian groups with an average condition on subgroups, J. Mahani Math. Res., vol 14 (2025), no. 1, 387-397.

B. Ebrahimzadeh, On the simple Suzuki group Sz(8) by the average order, Quasigroups Related Systems, vol. 33 (2025), no. 1, 19-22.

B. Ebrahimzadeh, F. Farazi, On the simple Suzuki group Sz(2^9) by the average order, Quasigroups Related Systems, vol. 33 (2025), no. 2, 227-230.

B. Taeri, Z. Tooshmalani, Finite groups with few average orders subgroups, 2025.

F. Di Concilio, On some functions on the order of the elements and of the commutators of a finite group, 2025.

On the sum of inverses of subgroup orders in finite groups, Sci. Stud. Res., Ser. Math. Inform., vol. 34 (2024), no. 1, 115-120, MR 4873479 (pdf).

On a group-theoretical generalization of the Euler's totient function, Indian J. Pure Appl. Math. vol. 55 (2024), no. 4, 1231-1233, MR 4832488, ZBL 1556.20036 (pdf).

On CLT and non-CLT groups, Ann. Mat. Pura Appl., vol. 203 (2024), no. 6, 2457-2462, MR 4813212, ZBL 1552.20124 (pdf), cited by:

K. Sharma, A.S. Reddy, CLT-groups with cyclic or abelian subgroups, 2024.

A.K.S. Sengar, On CLT and non-CLT numbers: classes and distribution, 2026.

A note on birdcage groups, Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar., vol. 86 (2024), no. 3, 41-46, MR 4805180 (pdf).

Completely realisable groups (with G. Fasolă), J. Algebra Appl., vol. 23 (2024), no. 10, article ID 2450163, MR 4783279, ZBL 1548.20032 (pdf).

Generalizing the Lehmer's totient problem, Elem. Math., vol. 79 (2024), no. 2, 77-79, MR 4733291, ZBL 1542.20107 (pdf).

On groups occurring as absolute centers of finite groups (with G. Fasolă), Comm. Algebra, vol. 52 (2024), no. 5, 1826-1831, MR 4716792, ZBL 1536.20034 (pdf), cited by:

M. Brescia, On the absolute centre and the autocommutator subgroup of a group, 2025.

Finite groups with few non-isolated subgroups, Publ. Math. Debrecen, vol. 103 (2023), no. 1-2, 165-170, MR 4654326, ZBL 1538.20014 (pdf).

Finite groups with large Chermak-Delgado lattices (with G. Fasolă), Bull. Aust. Math. Soc., vol. 107 (2023), no. 3, 451-455, MR 4586086, ZBL 1521.20045 (pdf), cited by:

D. Burrell, Computation of finite groups, Ph. D. Thesis, University of Florida, USA, 2023.

G. Liu, H. Qu, L. An, Finite p-groups with at most p^2+p subgroups not in Chermak-Delgado lattice, 2023.

W. Cocke, R. McCulloch, Central products and the Chermak-Delgado lattice, J. Pure Appl. Algebra, vol. 228 (2024), no. 12, article ID 107769.

D. Burrell, W. Cocke, R. McCulloch, On groups with few subgroups not in the Chermak-Delgado lattice, Arnold Math. J., vol. 10 (2024), no. 2, 265-279.

G. Liu, Q. Song, Finite groups with at most six subgroups not in the Chermak-Delgado lattice, Electron. Res. Arch., vol. 33 (2025), no. 9, 5769-5775.

G. Liu, H. Qu, L. An, Finite groups with the most Chermak-Delgado measures of subgroups, Comm. Algebra, vol. 54 (2026), no. 5, 1908-1917.

J. Lu, X. Huang, Q. Lian, W. Meng, Finite groups with few subgroups not in the Chermak-Delgado lattice, J. Group Theory, vol. 29 {2026), no. 1, 185-194.

On the number of edges of cyclic subgroup graphs of finite groups, Arch. Math., vol. 120 (2023), no. 4, 349-353, MR 4561107, ZBL 1512.20076 (pdf), cited by:

K. Sharma, A.S. Reddy, Cyclic subgroup graph of a group, 2024.

S. Malviy, V. Kakkar, S. Srivastava, Line graph characterization of cyclic subgroup graph, 2025.

S. Malviy, M. Patidar, J. Meher, V. Kakkar, Forbidden subgraphs of cyclic subgroup graphs of finite groups, 2025.

G. Fasolă, On subgroup graphs of finite abelian groups, Acta Univ. Sapientiae, vol. 18 (2026), no. 1, article ID 30.

A.J. Barios, E. Gonzales-Jimenez, I. Novak, Isogeny graphs of eliptic curves in characteristic zero, 2026.

Addendum to "A generalization of a result on the sum of element orders of a finite group" (with M.S. Lazorec), Math. Slovaca, vol. 73 (2023), no. 1, 65-68, MR 4548300, ZBL 1544.20045 (pdf), cited by:

M.S. Lazorec, A set theoretic version of equations on groups, 2026.

On a group-theoretical generalization of the Gauss formula (with G. Fasolă), Czech. Math. J., vol. 73 (2023), no. 1, 311-317, MR 4541104, ZBL 07655770 (pdf), cited by:

R. McCulloch, An answer regarding automorphisms of finite abelian groups, 2026.

On the average order of a finite group (with M.S. Lazorec), J. Pure Appl. Algebra, vol. 227 (2023), no. 4, article ID 107276, MR 4512539, ZBL 1521.20050 (pdf), cited by:

M. Maj, Detecting properties of a finite group through the study of some functions on element orders, Ural Seminar Group Theory Combin., Yekaterinburg, Russia, 2022.

M. Herzog, P. Longobardi, M. Maj, On groups with average element orders equal to the average order of the alternating group of degree 5, Glasnik Mat., vol. 58 (2023), no. 2, 307-315.

G.A. Miranda, Sobre a ordem média de grupos finitos, Master Thesis, Universidade de Brasilia, Brasilia, 2023.

A. Zarezadeh, B. Khosravi, Z. Akhlaghi, Characterizing some finite groups by the average order, Quaest. Math., vol. 47 (2024), no. 11, 2259-2270.

S. Sarkar, Average order in regular wreath products, Int. J. Group Theory, vol. 13 (2024), no. 2, 195-202.

A. Khandran, K.V. Namboothiri, V. Sivadasan, A density theorem related to dihedral groups, Bull. Korean Math. Soc., vol. 61 (2024), no. 3, 611-619.

P. Piwek, Solvable and non-solvable finite groups of the same order type, Algebra Number Theory, vol. 19 (2025), no. 8, 1663-1670.

B. Taeri, Z. Tooshmalani, Finite groups with few average orders subgroups, 2025.

F. Di Concilio, On some functions on the order of the elements and of the commutators of a finite group, 2025.

Another Menon-type identity derived from group actions, Sci. Stud. Res., Ser. Math. Inform., vol. 32 (2022), no. 1, 99-104, MR 4580628, ZBL 1549.11010 (pdf).

On the supersolvability of a finite group by the sum of subgroup orders, J. Algebra Appl., vol. 21 (2022), no. 12, article ID 2250232, MR 4500320, ZBL 1509.20035 (pdf), cited by:

L. Cui, W. Meng, J. Lu, W. Zheng, A new criterion for solvability of a finite group by the sum of non-normal subgroups orders, Colloq. Math., vol. 174 (2023), 169-176.

W. Meng, J. Lu, On the sum of non-cyclic subgroups order in a finite group, Comm. Algebra, vol. 52 (2024), no. 3, 1084-1096.

H. Chen, B. Zhang, W. Meng, On the sum of orders of non-cyclic and non-normal subgroups in a finite group, Int. Electron. J. Algebra, vol. 36 (2024), 206-214.

Groups whose same-order types are arithmetic progressions (with M.S. Lazorec), Quaest. Math., vol. 45 (2022), no. 8, 1309-1316, MR 4492938, ZBL 1514.20086 (pdf), cited by:

C. Anabanti, R. Shen, Arithmetic progressions of same order type in 2-groups, 2023.

Y. Jin, Finite 2-roups whose the same-order type is arithmetic progressions, Eur. J. Math. Appl., vol. 4 (2024), article ID 21.

Y. Jin, R. Shen, Groups whose same-order types are arithmetic progressions, Int. J. Group Theory, vol. 14 (2025), no. 3, 165-170.

Arithmetic progressions in finite groups, Asian-Eur. J. Math., vol. 15 (2022), no. 5, article ID 2250096, MR 4429690, ZBL 1491.20066 (pdf), cited by:

C. Anabanti, R. Shen, Arithmetic progressions of same order type in 2-groups, 2023.

Another criterion for supersolvability of finite groups, J. Algebra, vol. 604 (2022), 682-693, MR 4416728, ZBL 1520.20035 (pdf), cited by:

M. Maj, Detecting properties of a finite group through the study of some functions on element orders, Ural Seminar Group Theory Combin., Yekaterinburg, Russia, 2022.

M.B. Azad, B. Khosravi, H. Rashidi, On the sum of the inverses of the element orders in finite groups, Comm. algebra, vol. 51 (2023), no. 2, 694-698.

M. Herzog, P. Longobardi, M. Maj, On groups with average element orders equal to the average order of the alternating group of degree 5, Glasnik Mat., vol. 58 (2023), no. 2, 307-315.

A. Zarezadeh, B. Khosravi, Z. Akhlaghi, Characterizing some finite groups by the average order, Quaest. Math., vol. 47 (2024), no. 11, 2259-2270.

M. Kuang, J. Lu, W. Meng, B. Zhang, Some criteria for solvability in finite groups, Italian J. Pure Appl. Math., vol 52 (2024), 86-92

B. Taeri, Z. Tooshmalani, Minimal non-abelian groups with an average condition on subgroups, J. Mahani Math. Res., vol 14 (2025), no. 1, 387-397.

B. Taeri, Z. Tooshmalani, Finite groups with few average orders subgroups, 2025.

F. Di Concilio, On some functions on the order of the elements and of the commutators of a finite group, 2025.

M.B. Azad, M. Arabtash, Identifying structural characteristics of finite groups by the sum of their element orders, 2025.

On the size of coset unions (with B. Sambale), J. Algebraic Combin., vol. 55 (2022), no. 3, 979-987, MR 4412366, ZBL 1498.20060 (pdf), cited by:

R.P. Panda, On set difference of maximal cyclic subgroups of a p-group, 2023.

B. Sambale, On redundant Sylow subgroups, J. Algebra, vol. 650 (2024), 1-9.

A. Maróti, J. Martinez, A. Moretó, Covering the set of p-elements in finite groups by Sylow p-subgroups, J. Algebra, vol. 638 (2024), 840-861.

B. Sambale, On the complement of a union of cosets, 2026.

Isolated subgroups of finite abelian groups, Czech. Math. J., vol. 72 (2022), no. 2, 615-620, MR 4412778, ZBL 07547223 (pdf).

A new Menon-type identity derived from group actions, Sci. Stud. Res., Ser. Math. Inform., vol. 31 (2021), no. 2, 73-76, MR 4414955, ZBL 1549.11009 (pdf), cited by:

L. Tóth, Proofs, generalizations and analogs of Menon's identity: a survey, Acta Univ. Sapientiae, vol. 15 (2023), no. 1, 142-197.

A generalization of a result on the sum of element orders of a finite group, Math. Slovaca, vol. 71 (2021), no. 3, 627-630, MR 4272885, ZBL 1539.20012 (pdf), cited by:

S. Saha, A generalization of a result on the sum of the powers of the element orders of a finite group, 2021.

A. Olayiwola, S.A. Adebisi, F.I. Zakari, Classification of finite dicyclic groups by sum of element orders, Sule Lamido Univ. J. Sci. Tech., vol. 10 (2025), no. 2, 46-48.

S. Saha, Some characterization of finite groups using the sum of power of element orders, 2026.

M.S. Lazorec, A set theoretic version of equations on groups, 2026.

A characterization of the quaternion group by the sum of subgroup orders, Int. J. Open Problems Compt. Math., vol. 14 (2021), no. 2, 15-19 (pdf), cited by:

S.A. Adebisi, M. Enioluwafe, The existence of convexity in group actions Trans. J. Math. Analysis Appl., vol. 10 (2022), no. 1, 27-37.

A. Olayiwola, S.A. Adebisi, On the sum of subgroup orders of a class of dicyclic groups Sule Lamido Univ. J. Sci. Tech., vol. 10 (2022), no. 2, 63-66.

A criterion for nilpotency of a finite group by the sum of element orders, Comm. Algebra, vol. 49 (2021), no. 4, 1571-1577, MR 4224676, ZBL 1515.20126 (pdf), cited by:

M. Maj, On the function sum of element orders in a finite group, SandGAL 2019, Cremona, Italy, 2019.

M.B. Azad, M. Jafarpour, B. Khosravi, A criterion for p-solvability, where p = 7 or p = 11, 2020.

M.B. Azad, B. Khosravi, Properties of finite groups determined by the product of their element orders, Bull. Aust. Math. Soc., vol. 103 (2021), no. 1, 88-95.

M.S. Lazorec, On a divisibility property involving the sum of element orders, Bull. Malays. Math. Sci. Soc., vol. 44 (2021), no. 2, 941-951.

M. Herzog, New criteria for solvability, nilpotency and other properties of finite groups, ISCHIA Group Theory Conference, 2021.

M.B. Azad, B. Khosravi, On two conjectures about the sum of element orders, Canad. Math. Bull., vol. 65 (2022), no. 1, 30-38.

M.B. Azad, M. Jafarpour, B. Khosravi, An answer to a conjecture on the sum of element orders, J. Algebra Appl., vol. 21 (2022), no. 4, article ID 2250067.

M. Maj, Detecting properties of a finite group through the study of some functions on element orders, Ural Seminar Group Theory Combin., Yekaterinburg, Russia, 2022.

B. Taeri, Z. Tooshmalani, Average order elements of finite groups, 2022.

M. Herzog, P. Longobardi, M. Maj, New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups, Int. J. Group Theory, vol. 12 (2023), no. 1, 35-44.

M.B. Azad, B. Khosravi, H. Rashidi, On the sum of the inverses of the element orders in finite groups, Comm. algebra, vol. 51 (2023), no. 2, 694-698.

M.S. Lazorec, Subgroups with a small sum of element orders, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., vol. 117 (2023), article ID 148.

M. Herzog, P. Longobardi, M. Maj, On groups with average element orders equal to the average order of the alternating group of degree 5, Glasnik Mat.. vol. 58 (2023), no. 2, 307-315.

M.S. Lazorec, A graph related to the sum of element orders of a finite group, Contributions to Discrete Math., vol. 18 (2023), no. 2, 113-128.

M.S. Lazorec, Element orders in extraspecial groups, Acta Math. Hung., vol. 173 (2024), 434-447.

A. Simonyi, Distribution of element orders in finite groups, Bachelor Thesis, Eótvós Loránd University, Budapesta, 2025.

A. Olayiwola, S.A. Adebisi, F.I. Zakari, Classification of finite dicyclic groups by sum of element orders, Sule Lamido Univ. J. Sci. Tech., vol. 10 (2025), no. 2, 46-48.

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L. Iorio, M. Trombetti, Finite groups with a large normalized sum of element orders, J. Algebraic Combin., vol. 64 (2026), no. 1, article ID 6.

M.S. Lazorec, On some problems regarding LCM-groups, 2026.

S. Pooyandeh, L. Oftadeh, The effect of the sum of the inverse-power of element orders on finite groups, 2026.

S. Chatterjee, A. Das, Cyclic probability of a finite group, 2026.

On some probabilistic aspects of (generalized) dicyclic groups (with M.S. Lazorec), Quaest. Math., vol. 44 (2021), no. 1, 129-146, MR 4211983, ZBL 1505.20064 (pdf), cited by:

M.S. Lazorec, Probabilistic aspects of ZM-groups, Comm. Algebra, vol. 47 (2019), no. 2, 541-552.

S. Mitkari, V. Kharat, On the lattice of pronormal subgroups of dicyclic, alternating and symmetric groups, Math. Bohemica, vol. 149 (2024), no. 3, 427-438.

The second minimum/maximum value of the number of cyclic subgroups of finite p-groups (with M.S. Lazorec and R. Shen), Bull. Aust. Math. Soc., vol. 103 (2021), no. 1, 96-103, MR 4205764, ZBL 1498.20058 (pdf), cited by:

S.A. Adebisi, M. Ogiugo, Euler's totient function as applied to finding the number of cyclic subgroups of finite p-groups, Int. J. Math. Stat. Op. Res., vol. 1 (2021), no. 2, 163-167.

S.A. Adebisi, M. Ogiugo, The Euler's totient function and the general group theory, Pure Appl. Analysis, vol. 2022, article ID 3.

J. Liu, J. Ma, W. Meng, On the number of non-cyclic subgroups of finite p-groups, 2026.

A result on the number of cyclic subgroups of a finite group, Proc. Japan Academy, Ser. A, vol. 96 (2020), no. 10, 93-94, MR 4184277, ZBL 1509.20034 (pdf), cited by:

H.B. Shelash, H.J. Mehdi, Computing the certain subgroups of the group D_{2n} × C_p, where p is an odd prime, J. Physics, Conference Series, vol. 1818 (2021), no. 1, article ID 012081.

M. Herzog, New criteria for solvability, nilpotency and other properties of finite groups, ISCHIA Group Theory Conference, 2021.

M. Herzog, P. Longobardi, M. Maj, New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups, Int. J. Group Theory, vol. 12 (2023), no. 1, 35-44.

On the solvability of a finite group by the sum of subgroup orders, Bull. Korean Math. Soc., vol. 57 (2020), no. 6, 1475-1479, MR 4180189, ZBL 1498.20061 (pdf), cited by:

M. Herzog, P. Longobardi, M. Maj, On a criterion for solvability of a finite group, Comm. Algebra, vol. 49 (2021), no. 5, 2234-2240.

M. Herzog, New criteria for solvability, nilpotency and other properties of finite groups, ISCHIA Group Theory Conference, 2021.

M. Herzog, P. Longobardi, M. Maj, New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups, Int. J. Group Theory, vol. 12 (2023), no. 1, 35-44.

L. Cui, W. Meng, J. Lu, W. Zheng, A new criterion for solvability of a finite group by the sum of non-normal subgroups orders, Colloq. Math., vol. 174 (2023), 169-176.

W. Meng, J. Lu, On the sum of non-cyclic subgroups order in a finite group, Comm. Algebra, vol. 52 (2024), no. 3, 1084-1096.

H. Chen, B. Zhang, W. Meng, On the sum of orders of non-cyclic and non-normal subgroups in a finite group, Int. Electron. J. Algebra, vol. 36 (2024), 206-214.

A. Olayiwola, S.A. Adebisi, On the sum of subgroup orders of a class of dicyclic groups Sule Lamido Univ. J. Sci. Tech., vol. 10 (2022), no. 2, 63-66.

Detecting structural properties of finite groups by the sum of element orders, Israel J. Math., vol. 238 (2020), no. 2, 629-637, MR 4145812, ZBL 1483.20048 (pdf), cited by:

M.B. Azad, B. Khosravi, A criterion for p-nilpotency and p-closedness by the sum of element orders, Comm. Algebra, vol. 48 (2020), no. 12, 5391-5395.

M.B. Azad, M. Jafarpour, B. Khosravi, A criterion for p-solvability, where p = 7 or p = 11, 2020.

M.B. Azad, B. Khosravi, Properties of finite groups determined by the product of their element orders, Bull. Aust. Math. Soc., vol. 103 (2021), no. 1, 88-95.

M. Herzog, New criteria for solvability, nilpotency and other properties of finite groups, ISCHIA Group Theory Conference, 2021.

A.A. Buturlakin, A.E. Tereshchenko, The sum of orders of elements in nonabelian groups of odd order, Siberian Electron. Math. Reports, vol. 18 (2021), no. 2, 1698-1704.

M. Norman, A group-theoretical approach to Lehmer's totient problem, 2021.

M.B. Azad, B. Khosravi, On two conjectures about the sum of element orders, Canad. Math. Bull., vol. 65 (2022), no. 1, 30-38.

M.B. Azad, M. Jafarpour, B. Khosravi, An answer to a conjecture on the sum of element orders, J. Algebra Appl., vol. 21 (2022), no. 4, article ID 2250067.

H.K. Dey, The solvability of a finite group by the sum of powers of element orders, 2022.

M. Herzog, P. Longobardi, M. Maj, New criteria for solvability, nilpotency and other properties of finite groups in terms of the order elements or subgroups, Int. J. Group Theory, vol. 12 (2023), no. 1, 35-44.

M.B. Azad, B. Khosravi, H. Rashidi, On the sum of the inverses of the element orders in finite groups, Comm. algebra, vol. 51 (2023), no. 2, 694-698.

M. Herzog, P. Longobardi, M. Maj, On groups with average element orders equal to the average order of the alternating group of degree 5, Glasnik Mat., vol. 58 (2023), no. 2, 307-315.

M.S. Lazorec, A graph related to the sum of element orders of a finite group, Contributions to Discrete Math., vol. 18 (2023), no. 2, 113-128.

H.K. Dey, A. Mondal, An exact upper bound for the sum of powers of element orders in non-cyclic finite groups, J. Pure Appl. Algebra, vol. 228 (2024), no. 6, article ID 107580.

V. Grazian, C. Monetta, M. Noce, On the structure of finite groups determined by arithmetic and geometric means of element orders, Comm. Algebra, vol. 52 (2024), no. 7, 2715-2723.

A. Khandran, K.V. Namboothiri, V. Sivadasan, A density theorem related to dihedral groups, Bull. Korean Math. Soc., vol. 61 (2024), no. 3, 611-619.

M. Kuang, J. Lu, W. Meng, B. Zhang, Some criteria for solvability in finite groups, Italian J. Pure Appl. Math., vol 52 (2024), 86-92.

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