On the group pseudo-algebra of finite groups

Mark L. Lewis; Quanfu Yan

doi:10.5802/crmath.671

Article de recherche - Théorie des groupes, Théorie des représentations

On the group pseudo-algebra of finite groups
[Sur la pseudo-algèbre de groupe des groupes finis]

Mark L. Lewis ¹ ; Quanfu Yan ^1,²

¹ Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
² School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1661-1665.

Résumé
Abstract

Soit $G$ un groupe fini. La pseudo-algèbre de groupe de G est définie comme le multi-ensemble $C (G) = {(d, m_{G} (d)) ∣ d \in Cod (G)}$ , où $m_{G} (d)$ est le nombre de caractères irréductibles de $G$ de codegré $d \in Cod (G)$ . Nous montrons qu’il existe deux p-groupes finis avec des ordres distincts qui ont la même pseudo-algèbre de groupe, ce qui fournit une réponse à la question 3.2 de [7]. De plus, nous discutons également sous quelles hypothèses deux p-groupes ayant la même pseudo-algèbre de groupe sont forcément isomorphes.

Let $G$ be a finite group. The group pseudo-algebra of $G$ is defined as the multi-set $C (G) = {(d, m_{G} (d)) ∣ d \in Cod (G)}$ , where $m_{G} (d)$ is the number of irreducible characters of $G$ with codegree $d \in Cod (G)$ . We show that there exist two finite $p$ -groups with distinct orders that have the same group pseudo-algebra, providing an answer to Question 3.2 in [7]. In addition, we also discuss under what hypothesis two $p$ -groups with the same group pseudo-algebra will be isomorphic.

Reçu le : 2024-05-11
Révisé le : 2024-07-16
Accepté le : 2024-07-26
Publié le : 2024-11-25

DOI : 10.5802/crmath.671

Classification : 20C15, 20D15
Keywords: Finite $p$-groups, Characters, Group pseudo-algebra
Mots-clés : p-groupes finis, Caractères, Pseudo-algèbre de groupe

Affiliations des auteurs :

Mark L. Lewis ¹ ; Quanfu Yan ^{1, 2}

¹ Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
² School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {On the group pseudo-algebra of finite groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1661--1665},
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Mark L. Lewis; Quanfu Yan. On the group pseudo-algebra of finite groups. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1661-1665. doi : 10.5802/crmath.671. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.671/

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