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(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.