Comptes Rendus
no. 4
Group theory
Counting the number of supercharacter theories of a finite group
[Dénombrement des théories de supercaractères d'un groupe fini]

Présenté par : the Editorial Board

Ali Reza Ashrafi1 ; Fatemeh Koorepazan-Moftakhar1
1 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317 – 53153, Islamic Republic of Iran
Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 323-326.

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 2n, n≥3, 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 2n, n≥3, have the same number of supercharacter theories.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.03.005
Ali Reza Ashrafi 1 ; Fatemeh Koorepazan-Moftakhar 1

1 Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317 – 53153, Islamic Republic of Iran 
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Ali Reza Ashrafi; Fatemeh Koorepazan-Moftakhar. Counting the number of supercharacter theories of a finite group. Comptes Rendus. Mathématique, Volume 357 (2019) no. 4, pp. 323-326. doi : 10.1016/j.crma.2019.03.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.03.005/

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