The Influence of C- Z-permutable Subgroups on the Structure of Finite Groups

Authors

  • Mohammed Mosa Al-shomrani Northern Border University
  • Abdlruhman A. Heliel Beni-Suef University, Beni-Suef, Egypt

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i1.3184

Keywords:

permutable subgroups, C-Z-permutable subgroups of G, Sylow subgroup

Abstract

Let Z be a complete set of Sylow subgroups of a ï¬nite group G, that is, for each prime p dividing the order of G, Z contains exactly one and only one Sylow p-subgroup of G, say Gp. Let C be a nonempty subset of G. A subgroup H of G is said to be C-Z-permutable (conjugateZ-permutable) subgroup of G if there exists some x ∈ C such that HxGp = GpHx, for all Gp ∈ Z. We investigate the structure of the ï¬nite group G under the assumption that certain subgroups of prime power orders of G are C-Z-permutable subgroups of G.

Author Biographies

Mohammed Mosa Al-shomrani, Northern Border University

Department of Mathematics, Faculty of Science, Northern Border University

Abdlruhman A. Heliel, Beni-Suef University, Beni-Suef, Egypt

Department of Mathematics, Faculty of Science 62511, Beni-Suef University, Beni-Suef, Egypt

Downloads

Published

2018-01-30

How to Cite

Al-shomrani, M. M., & Heliel, A. A. (2018). The Influence of C- Z-permutable Subgroups on the Structure of Finite Groups. European Journal of Pure and Applied Mathematics, 11(1), 160–168. https://doi.org/10.29020/nybg.ejpam.v11i1.3184

Issue

Vol. 11 No. 1: (January 2018)

Section

Game Theory

License

Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.