Normalized unit groups and their conjugacy classes

Abstract

Let G = H × A be a finite 2-group, where H is a non-abelian group of order 8 and A is an elementary abelian 2-group. We obtain a normal complement of G in the normalized unit group V(FG) and in the unitary subgroup V∗(FG) over the field F with 2 elements. Further, for a finite field F of characteristic 2, we derive class size of elements of V(FG). Moreover, we provide class representatives of V∗(F H).