Group Algebras Whose Involutory Units Commute (Dedicated to the memory of Professor I.I. Khripta)

• 来源期刊: 代数集刊（英文版）
• 关键词: group algebra group of units
• 年，卷（期）: 2002,（1）
• 页码范围: 49-64
• 页数: 16页
• 语种: 英文

摘要

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.