Number theory/Group theory
Revisiting the Leinster groups
[Quelques résultats sur les groupes de Leinster]
Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 1-6.

Un groupe de Leinster est un groupe fini tel que la somme des cardinaux de ses sous-groupes distingués soit égale au double du cardinal de G. Dans cette note, nous donnons quelques résultats nouveaux sur les groupes de Leinster.

A finite group is said to be a Leinster group if the sum of the orders of its normal subgroups equals twice the order of the group itself. In this paper we give some new results concerning Leinster groups.

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Accepté le :
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DOI : 10.1016/j.crma.2013.11.009
Baishya, Sekhar Jyoti 1

1 Department of Mathematics, North-Eastern Hill University, Permanent Campus, Shillong-793022, Meghalaya, India
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Baishya, Sekhar Jyoti. Revisiting the Leinster groups. Comptes Rendus. Mathématique, Tome 352 (2014) no. 1, pp. 1-6. doi : 10.1016/j.crma.2013.11.009. http://www.numdam.org/articles/10.1016/j.crma.2013.11.009/

[1] Ashrafi, A.R. Counting the centralizers of some finite groups, Korean J. Comput. Appl. Math., Volume 7 (2000) no. 1, pp. 115-124

[2] Baishya, S.J. On finite groups with specific number of centralizers, Int. Electron. J. Algebra, Volume 13 (2013), pp. 53-62

[3] Baishya, S.J.; Das, A.K. Harmonic numbers and finite groups, Rend. Semin. Mat. Univ. Padova (2013) http://rendiconti.math.unipd.it/forthcoming.php?lan=english#BaishyaDas (in press)

[4] Das, A.K. On arithmetic functions of finite groups, Bull. Aust. Math. Soc., Volume 75 (2007), pp. 45-58

[5] Dolfi, S.; Herzog, M.; Jabara, E. Finite groups whose non-central commuting elements have centralizers of equal size, Bull. Aust. Math. Soc., Volume 82 (2010), pp. 293-304

[6] Leinster, T. Perfect numbers and groups, April 2001 | arXiv

[7] Lescot, P. Central extensions and commutativity degree, Comm. Algebra, Volume 29 (2001) no. 10, pp. 4451-4460

[8] MathOverflow http://mathoverflow.net/questions/54851

[9] Medts, T.D.; Maróti, A. Perfect numbers and finite groups, Rend. Semin. Mat. Univ. Padova, Volume 129 (2013), pp. 17-33

[10] Medts, T.D.; Tărnăuceanu, M. Finite groups determined by an inequality of the orders of their subgroups, Bull. Belg. Math. Soc. Simon Stevin, Volume 15 (2012) no. 4, pp. 699-704

[11] Ore, O. On the averages of the divisors of a number, Amer. Math. Monthly, Volume 55 (1948), pp. 615-619

[12] Tărnăuceanu, M. Finite groups determined by an inequality of the orders of their normal subgroups, An. Ştiinţ. Univ. “Al.I. Cuza” Iaşi, Mat., Volume 57 (2011), pp. 229-238

[13] The GAP Group GAP – Groups, Algorithms, and Programming, Version 4.6.4, 2013 http://www.gap-system.org

[14] Wall, C.T.C. On groups consisting mostly of involutions, Proc. Camb. Philos. Soc., Volume 67 (1970), pp. 251-262

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