Class length of elements of group in the normalized unit group

Abstract

Let F be a finite field of characteristic p > 0. In this article, we obtain a relation between the class length of elements of a finite p-group G in the normalized unit group V (F G) and its unitary subgroup V∗(F G), 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 (F G), 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 .