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

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Published

2018-01-30

Issue

Vol. 11 No. 1: (January 2018)

Section

Game Theory

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How to Cite

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