О неприводимых представлениях разрешимых групп конечного ранга над локально конечным полем

Abstract

We consider the representations of soluble groups of finite rank over a locally finite field. We found some necessary and some sufficient conditions for the existence of the faithful irreducible representations of soluble groups of finite rank over a locally finite field. The construction of an Abelian socle and a minimally infinite socle of soluble groups of finite rank plays the most important role in the conditions for the existence of such representations.