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Ricerche di Matematica

, Volume 68, Issue 2, pp 571–579 | Cite as

On weakly s-semipermutable or ss-quasinormal subgroups of finite groups

  • Qingjun KongEmail author
  • Xiuyun Guo
Article
  • 40 Downloads

Abstract

Suppose that G is a finite group and H is a subgroup of G. H is said to be weakly s-semipermutable in G if there are a subnormal subgroup T of G and an s-semipermutable subgroup \(H_{ssG}\) of G contained in H such that \(G=HT\) and \(H\cap T\le H_{ssG}\); H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that \(G=HB\) and H permutes with every Sylow subgroup of B. We fix in every non-cyclic Sylow subgroup P of G some subgroup D satisfying \(1<|D|<|P|\) and study the structure of G under the assumption that every subgroup H of P with \(|H|=|D|\) is either weakly s-semipermutable or ss-quasinormal in G. Some recent results are generalized and unified.

Keywords

Weakly s-semipermutable subgroup ss-quasinormal subgroup Saturated formation 

Mathematics Subject Classification

20D10 20D20 

Notes

Acknowledgements

The paper is dedicated to Professor József Szabados for his 80th birthday. The authors thank the referee for his/her valuable suggestions. It should be said that we could not have polished the final version of this paper well without their outstanding efforts.

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Copyright information

© Università degli Studi di Napoli "Federico II" 2018

Authors and Affiliations

  1. 1.Department of MathematicsTianjin Polytechnic UniversityTianjinPeople’s Republic of China
  2. 2.Department of MathematicsShanghai UniversityShanghaiPeople’s Republic of China

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