2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59833Let 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.15 pages, AMS-TeXRings and AlgebrasGroup Theorytext