[Dénombrement des théories de supercaractères d'un groupe fini]
La théorie des supercaractères d'un groupe fini est une généralisation de la théorie des caractères ordinaires des groupes finis, introduite par Diaconis et Isaacs en 2008. Nous présentons ici le concept de groupes ayant des tables de caractères quasi identiques. Nous montrons également que les groupes avec des tables de caractères quasi identiques ont le même nombre de théories de supercaractères. En particulier, les groupes dihédraux et semi-dihédraux d'ordre , , ont le même nombre de théories de supercaractères.
The supercharacter theory of a finite group is a generalization of the ordinary character theory of finite groups that was introduced by Diaconis and Isaacs in 2008. In this paper, the concept of groups with quasi-identical character tables are presented. It is proved that the groups with quasi-identical character tables have the same number of supercharacter theories. As a consequence, the dihedral and semi-dihedral groups of order , , have the same number of supercharacter theories.
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@article{CRMATH_2019__357_4_323_0,
author = {Ashrafi, Ali Reza and Koorepazan-Moftakhar, Fatemeh},
title = {Counting the number of supercharacter theories of a finite group},
journal = {Comptes Rendus. Math\'ematique},
pages = {323--326},
publisher = {Elsevier},
volume = {357},
number = {4},
year = {2019},
doi = {10.1016/j.crma.2019.03.005},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2019.03.005/}
}
TY - JOUR AU - Ashrafi, Ali Reza AU - Koorepazan-Moftakhar, Fatemeh TI - Counting the number of supercharacter theories of a finite group JO - Comptes Rendus. Mathématique PY - 2019 SP - 323 EP - 326 VL - 357 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2019.03.005/ DO - 10.1016/j.crma.2019.03.005 LA - en ID - CRMATH_2019__357_4_323_0 ER -
%0 Journal Article %A Ashrafi, Ali Reza %A Koorepazan-Moftakhar, Fatemeh %T Counting the number of supercharacter theories of a finite group %J Comptes Rendus. Mathématique %D 2019 %P 323-326 %V 357 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2019.03.005/ %R 10.1016/j.crma.2019.03.005 %G en %F CRMATH_2019__357_4_323_0
Ashrafi, Ali Reza; Koorepazan-Moftakhar, Fatemeh. Counting the number of supercharacter theories of a finite group. Comptes Rendus. Mathématique, Tome 357 (2019) no. 4, pp. 323-326. doi : 10.1016/j.crma.2019.03.005. http://www.numdam.org/articles/10.1016/j.crma.2019.03.005/
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