Wreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class

TL;DR

This paper investigates the structure of the unit group in modular group algebras of 2-groups of maximal class, revealing a wreath product section involving the commutator subgroup.

Contribution

It establishes that the unit group contains a section isomorphic to a wreath product of order two with the commutator subgroup, a novel structural insight.

Findings

Unit group contains a wreath product section

Structural characterization of unit groups in modular group algebras

Connection between unit group structure and group G's properties

Abstract

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of the group G.