Israel Journal of Mathematics

, Volume 136, Issue 1, pp 145–155 | Cite as

Permutability of minimal subgroups andp-nilpotency of finite groups

  • Guo Xiuyun
  • K. P. Shum


In this paper it is proved that ifp is a prime dividing the order of a groupG with (|G|,p − 1) = 1 andP a Sylowp-subgroup ofG, thenG isp-nilpotent if every subgroup ofPG N of orderp is permutable inN G (P) and whenp = 2 either every cyclic subgroup ofPG N of order 4 is permutable inN G (P) orP is quaternion-free. Some applications of this result are given.


Normal Subgroup Finite Group Maximal Subgroup Prime Order Cyclic Subgroup 
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Copyright information

© Hebrew University 2003

Authors and Affiliations

  1. 1.Department of MathematicsShanxi UniversityTaiyuanPR China
  2. 2.Department of MathematicsThe Chinese University of Hong KongHong KongP.R. China (SAR)

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