The normal complement problem and the structure of the unitary subgroup

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The normal complement problem and the structure of the unitary subgroup

Author : Dr Surinder Kaur

Year : 2020

Publisher : Taylor and Francis Inc.325 Chestnut St, Suite 800PhiladelphiaPA 19106

Source Title : Communications in Algebra

Document Type :

Abstract

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 (Formula presented.) where F is the field with p elements. Further, assume that (Formula presented.) where A is a finite abelian p-group and (Formula presented.) If F is any finite field of characteristic p, then we prove that G does not have a normal complement in (Formula presented.) and obtain the structure of the unitary subgroup (Formula presented.) Communicated by Sudarshan Kumar Sehgal.