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On partially s-permutable subgroups of finite groups

  • 1.

    School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

  • 2.

    School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

Cite this: JUSTC, 2014, 44(12): 975-981
https://doi.org/10.3969/j.issn.0253-2778.2014.12.002
Funds: Supported by NSFC (11371335, 11401264).
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  • Corresponding author:

    YU Xiaolong (corresponding author), male, born in 1984, PhD. Research field: finite group theory.

  • Received Date: March 23, 2014
  • Revised Date: June 06, 2014
  • Accepted Date: June 06, 2014
  • Published Date: December 29, 2014
    Abstract
  • Let H be a subgroup of G. H is said to be partially s-permutable in G provided G has a subnormal subgroup T such that G=HT and H∩T≤HsT, where HsT is the subgroup of H generated by all the subgroups of H which permute with all the Sylow subgroups of T. Here, partially s-permutable subgroups were used to study the structure of finite groups and some new criteria of p-nilpotent groups and p-supersoluble groups were obtained.
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