Notes on Finite Groups with Nearly S-permutable and Nearly S-permutable-Transitive Subgroups

Authors

  • Abdulaziz Mutlaq Alotaibi Department of Mathematics, College of Science and Humanities in Al-Kharj
  • Khalid Al-Tahat Arab Open University. Amman, jordan
  • Khaled Mustafa Aljamal Arab Open University. Amman, jordan

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6033

Keywords:

S-permutable subgroup, Sylow subgroup, permutable subgroup, nearly S-permutable subgroup.

Abstract

Let G be a finite group and let H be a subgroup of G. We called H is nearly S-permutable in G if for every prime p such that (p, |H|) =1 and every subgroup K of G containing H the normalizer NK(H) contains some Sylow p-subgroup of K. We shall denoted this by (H is NSP in G). We introduce the class of NSPT-groups as those groups in which nearly S-permutability is transitive among subgroups. Specifically, if A is NSP in B  and  B is NSP in G, then A is NSP in G. In this paper we study certain finite groups characterized by NSP and NSPT properties and we also compare specific subgroups with groups under study, supported by theorems and examples.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Algebra

License

Copyright (c) 2025 Abdulaziz Mutlaq Alotaibi, Khalid Al-Tahat, Khaled Mustafa Aljamal

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How to Cite

Notes on Finite Groups with Nearly S-permutable and Nearly S-permutable-Transitive Subgroups. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6033. https://doi.org/10.29020/nybg.ejpam.v18i3.6033