Following Isaacs (see [6, p. 94]), we call a normal subgroup N of a finite group G large, if , so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing large subgroups in finite groups (see Theorems A and C). We also consider the more specialised problems of finding large (non-abelian) nilpotent as well as abelian subgroups in soluble groups.
Suivant la terminologie introduite par Isaacs (voir [6], p. 94), nous disons qu'un sous-groupe distingué N d'un groupe fini G est grand si , de sorte que N est d'indice borné dans G. Notre but principal est d'établir des résultats permettant de produire de façon systématique des grands sous-groupes dans les groupes finis (voir les théorèmes A et C). Nous considérons également les problèmes plus particuliers qui se posent pour trouver de grands sous-groupes nilpotents (non commutatifs) ainsi que de grands sous-groupes commutatifs dans les groupes résolubles.
Accepted:
Published online:
@article{CRMATH_2018__356_3_253_0,
author = {Aivazidis, Stefanos and M\"uller, Thomas W.},
title = {Large subgroups in finite groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {253--257},
publisher = {Elsevier},
volume = {356},
number = {3},
year = {2018},
doi = {10.1016/j.crma.2018.01.020},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2018.01.020/}
}
TY - JOUR AU - Aivazidis, Stefanos AU - Müller, Thomas W. TI - Large subgroups in finite groups JO - Comptes Rendus. Mathématique PY - 2018 SP - 253 EP - 257 VL - 356 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2018.01.020/ DO - 10.1016/j.crma.2018.01.020 LA - en ID - CRMATH_2018__356_3_253_0 ER -
%0 Journal Article %A Aivazidis, Stefanos %A Müller, Thomas W. %T Large subgroups in finite groups %J Comptes Rendus. Mathématique %D 2018 %P 253-257 %V 356 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2018.01.020/ %R 10.1016/j.crma.2018.01.020 %G en %F CRMATH_2018__356_3_253_0
Aivazidis, Stefanos; Müller, Thomas W. Large subgroups in finite groups. Comptes Rendus. Mathématique, Volume 356 (2018) no. 3, pp. 253-257. doi : 10.1016/j.crma.2018.01.020. https://www.numdam.org/articles/10.1016/j.crma.2018.01.020/
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