Group algebras whose involutory units commute

2000/09/01 by Victor Bovdi, Bovdi, Victor, Michael Dokuchaev +1
Engineering · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.GR #math.RA

paper · pdf · doi:10.48550/arxiv.math/0009003

15 pages, AMS-TeX

arxiv created 2000/09/01 · openalex publication_date 2000/09/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a field of characteristic 2 and G a nonabelian locally finite 2-group. Let V(KG) be the group of units with augmentation 1 in the group algebra KG. An explicit list of groups is given, and it is proved that all involutions in V(KG) commute with each other if and only if G is isomorphic to one of the groups on this list. In particular, this property depends only on G and not at all on K.

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