Paper “On subgroups of hypercentral type of finite groups” published in Israel J. Math.

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A. Ballester-Bolinches, Luis M. Ezquerro, Alexander N. Skiba

On subgroups of hypercentral type of finite groups

Israel J. Math., 199 (2014), 259–265

http://dx.doi.org/10.1007/s11856-013-0030-y

Abstract

The main purpose of this paper is to analyze the influence on the structure of a finite group of some subgroups lying in the hypercenter. More precisely, we prove the following: Let

Paper “On subgroups of hypercentral type of finite groups” to appear in Israel J. Math.

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A. Ballester-Bolinches, Luis M. Ezquerro, Alexander N. Skiba

On subgroups of hypercentral type of finite groups

Israel J. Math.

http://dx.doi.org/10.1007/s11856-013-0030-y

Abstract

The main purpose of this paper is to analyze the influence on the structure of a finite group of some subgroups lying in the hypercenter. More precisely, we prove the following: Let F be a Baer-local formation. Given a group G and a normal subgroup E of G, let ZF (G) contain a p-subgroup A of E which is maximal being abelian and of exponent dividing pk, where k is some natural number, k = 1 if p = 2 and the Sylow 2-subgroups of E are non-abelian. Then E/ O p (E) ≤ ZF(G/ Op (E)) (Theorem 1). Some well-known results turn out to be consequences of this theorem.