Group algebras whose groups of normalized units have exponent 4

TL;DR

This paper characterizes specific p-groups for which the normalized units in their group algebra over a field of characteristic p have exponent 4, providing a complete classification.

Contribution

It offers a full description of locally finite p-groups with normalized units of exponent 4 in their group algebra, a novel classification in this area.

Findings

Characterization of p-groups with units of exponent 4

Complete classification of such groups

Insight into the structure of normalized units in group algebras

Abstract

We give a full description of locally finite p-groups G such that the normalized group of units V(FG) of the group algebra FG over a field F of characteristic p has exponent 4.