Ukrainian Mathematical Journal

, Volume 64, Issue 1, pp 102–109 | Cite as

SΦ-supplemented subgroups of finite groups

  • Xianhua Li
  • Tao Zhao
Article
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We call H an SΦ-supplemented subgroup of a finite group G if there exists a subnormal subgroup T of G such that G = HT and H ∩ T ≤ Φ(H), where Φ(H) is the Frattini subgroup of H. In this paper, we characterize the p-nilpotency and supersolubility of a finite group G under the assumption that every subgroup of a Sylow p-subgroup of G with given order is SΦ-supplemented in G: Some results about formations are also obtained.

Keywords

Normal Subgroup Maximal Subgroup Minimal Normal Subgroup Subnormal Subgroup Frattini Subgroup 
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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • Xianhua Li
    • 1
  • Tao Zhao
    • 2
  1. 1.School of Mathematical SciencesSoochow UniversitySuzhouChina
  2. 2.School of SciencesShandong University of TechnologyZiboChina

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