In this paper we study the structure of a group G = SH factorized by an elementary abelian group S of exponent 2 and a periodic group H without involutions. Our main result is Theorem. Let G = SH be a group factorized by S, a subgroup of exponent 2, and H, a periodic group without elements of even order. If H is hypercentral then G is hyperabelian; moreover, if H is soluble with derived length d, then G has derived length at most 2d.
A note on some factorized groups
JABARA, Enrico
2004-01-01
Abstract
In this paper we study the structure of a group G = SH factorized by an elementary abelian group S of exponent 2 and a periodic group H without involutions. Our main result is Theorem. Let G = SH be a group factorized by S, a subgroup of exponent 2, and H, a periodic group without elements of even order. If H is hypercentral then G is hyperabelian; moreover, if H is soluble with derived length d, then G has derived length at most 2d.
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