Counting the number of supercharacter theories of a finite group. (Dénombrement des théories de supercaractères d’un groupe fini.) (English. French summary) Zbl 1515.20042
Summary: The supercharacter theory of a finite group is a generalization of the ordinary character theory of finite groups that was introduced by P. Diaconis and I. M. Isaacs in 2008 [Trans. Am. Math. Soc. 360, No. 5, 2359–2392 (2008; Zbl 1137.20008)]. 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 \(2^n\), \(n \geq 3\), have the same number of supercharacter theories.
MSC:
| 20C15 | Ordinary representations and characters |
Citations:
Zbl 1137.20008Software:
GAPReferences:
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