The normal complement problem and the structure of the unitary subgroup

摘要

Let p be an odd prime and G be a finite split metabelian p-group of exponent p. In this article, we obtain a normal complement of G in where F is the field with p elements. Further, assume that where A is a finite abelian p-group and If F is any finite field of characteristic p, then we prove that G does not have a normal complement in and obtain the structure of the unitary subgroup V-*(FG).