CLASS LENGTH OF ELEMENTS OF GROUP IN THE NORMALIZED UNIT GROUP

Abstract

Let F be a finite field of characteristic p > 0. In this article, we

obtain a relation between the class length of elements of a finite p-group G in

the normalized unit group V(FG) and its unitary subgroup V*(FG), when p

is an odd prime. We also provide the size of the conjugacy class of non-central

elements of a group G in V(FG); where either G is any finite p-group with

nilpotency class 2 or G is a p-group with nilpotency class 3 such that |G|<= p^5.

Keywords

• Group ring,unit group,unitary units,conjugacy class

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