Group algebras whose involutory units commute

Bódi, Viktor and Dokuchaev, M. (2002) Group algebras whose involutory units commute. Algebra Colloquium, 9 (1). pp. 49-64. ISSN 1005-3867

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Abstract

Let K be a field of characteristic 2 and G a non-abelian 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 does not depend on K.

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