This article is cited in 5 papers

On the Prime Radical of $PI$-Representable Groups

S. A. Pikhtilkov

Tula State Pedagogical University

Abstract: The notion of $PI$-representable groups is introduced; these are subgroups of invertible elements of a $PI$-algebra over a field. It is shown that a $PI$-representable group has a largest locally solvable normal subgroup, and this subgroup coincides with the prime radical of the group. The prime radical of a finitely generated $PI$-representable group is solvable. The class of $PI$-representable groups is a generalization of the class of linear groups because in the groups of the former class the largest locally solvable normal subgroup can be not solvable.

UDC: 512.544.37

Received: 01.07.2001

DOI: 10.4213/mzm463

 English version: Mathematical Notes, 2002, 72:5, 682–686

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