Abstract
Let G be a finite group. A subgroup H of G is said to be s-conditionally permutable in G if, for every prime \(p\in \pi (G)\), there exists a Sylow p-subgroup P of G such that \({ HP}={ PH}\). The purpose here is to study the influence of s-conditional permutability of maximal subgroups of Sylow subgroups on the p-nilpotence of finite groups. Some known results are generalized.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Asaad, M.: On maximal subgroups of Sylow subgroups of finite groups. Commun. Algebra 26, 3647–3652 (1998)
Huang, J., Guo, W.: \(s\)-Conditionally permutable subgroups of finite groups. Ann. Math. China A 28, 17–26 (2007)
Kegel, O.H.: Sylow–Gruppen und Subnormalteiler endlicher Gruppen. Math. Z. 78, 205–221 (1962)
Robinson, D.J.S.: A Course in the Theory of Groups. Springer, New York (1980)
Shaalan, A.: The influence of \(\pi \)-quasinormality of some subgroups on the structure of a finite group. Acta Math. Hungar. 56, 287–293 (1990)
Srinivasan, S.: Two sufficient conditions for supersolvability of finite groups. Isr. J. Math. 35, 210–224 (1980)
Acknowledgements
The authors are very grateful to the referee and Prof. John S. Wilson who pointed out several linguistic errors and provided many valuable suggestions and comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by A. Constantin.
The paper is dedicated to Professor John Cossey for his 75th birthday.
The research of the authors is supported by the National Natural Science Foundation of China (11201400).
Rights and permissions
About this article
Cite this article
Kang, P., Pan, H. On s-conditional permutability of maximal subgroups of Sylow subgroups of finite groups. Monatsh Math 187, 109–112 (2018). https://doi.org/10.1007/s00605-017-1088-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-017-1088-0