Israel Journal of Mathematics

, Volume 199, Issue 1, pp 259–265 | Cite as

On subgroups of hypercentral type of finite groups

  • A. Ballester-Bolinches
  • Luis M. Ezquerro
  • Alexander N. Skiba
Article

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\(\mathfrak{F}\)be a Baer-local formation. Given a group G and a normal subgroup E of G, let\(Z_\mathfrak{F} (G)\)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/Op (E) ≤ \(Z_\mathfrak{F} \)(G/Op (E)) (Theorem 1). Some well-known results turn out to be consequences of this theorem.

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Copyright information

© Hebrew University Magnes Press 2014

Authors and Affiliations

  • A. Ballester-Bolinches
    • 1
  • Luis M. Ezquerro
    • 2
  • Alexander N. Skiba
    • 3
  1. 1.Departament d’ÀlgebraUniversitat de ValènciaBurjassot, ValènciaSpain
  2. 2.Departamento of MatemáticasUniversidad Pública de NavarraPamplona, NavarraSpain
  3. 3.Department of MathematicsGomel State University F. SkorinaGomelBelarus

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