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SΦ-supplemented subgroups of finite groups

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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 HT ≤ 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.

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Author information

Correspondence to Xianhua Li.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64 No. 1 pp. 92–99 January 2012.

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Li, X., Zhao, T. SΦ-supplemented subgroups of finite groups. Ukr Math J 64, 102–109 (2012). https://doi.org/10.1007/s11253-012-0632-2

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Keywords

  • Normal Subgroup
  • Maximal Subgroup
  • Minimal Normal Subgroup
  • Subnormal Subgroup
  • Frattini Subgroup