Comptes Rendus
Number theory/Group theory
Revisiting the Leinster groups
[Quelques résultats sur les groupes de Leinster]
Comptes Rendus. Mathématique, Volume 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.

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

1 Department of Mathematics, North-Eastern Hill University, Permanent Campus, Shillong-793022, Meghalaya, India
@article{CRMATH_2014__352_1_1_0,
     author = {Sekhar Jyoti Baishya},
     title = {Revisiting the {Leinster} groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1--6},
     publisher = {Elsevier},
     volume = {352},
     number = {1},
     year = {2014},
     doi = {10.1016/j.crma.2013.11.009},
     language = {en},
}
TY  - JOUR
AU  - Sekhar Jyoti Baishya
TI  - Revisiting the Leinster groups
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 1
EP  - 6
VL  - 352
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crma.2013.11.009
LA  - en
ID  - CRMATH_2014__352_1_1_0
ER  - 
%0 Journal Article
%A Sekhar Jyoti Baishya
%T Revisiting the Leinster groups
%J Comptes Rendus. Mathématique
%D 2014
%P 1-6
%V 352
%N 1
%I Elsevier
%R 10.1016/j.crma.2013.11.009
%G en
%F CRMATH_2014__352_1_1_0
Sekhar Jyoti Baishya. Revisiting the Leinster groups. Comptes Rendus. Mathématique, Volume 352 (2014) no. 1, pp. 1-6. doi : 10.1016/j.crma.2013.11.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.11.009/

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

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

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

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

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

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

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

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

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

[10] T.D. Medts; M. Tărnăuceanu 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] O. Ore On the averages of the divisors of a number, Amer. Math. Monthly, Volume 55 (1948), pp. 615-619

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

Cité par Sources :

Commentaires - Politique


Ces articles pourraient vous intéresser

Sylow 2-subgroups of solvable Q1-groups

Meysam Norooz-Abadian; Hesamuddin Sharifi

C. R. Math (2017)


A new canonical induction formula for p-permutation modules

Laurence Barker; Hatice Mutlu

C. R. Math (2019)