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ON CONJUGATE-ℨ-PERMUTABLE SUBGROUPS OF FINITE GROUPS

A. A. HELIEL

Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia

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

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and

T.M. Al-GAFRI

Department of Mathematics, Faculty of Science 80203, King Abdulaziz University, Jeddah 21589, Saudi Arabia

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https://doi.org/10.1142/S0219498813500606Cited by:2 (Source: Crossref)

Abstract

Let ℨ be a complete set of Sylow subgroups of a finite 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 G_p. Let C be a nonempty subset of G. A subgroup H of G is said to be C-ℨ-permutable (conjugate-ℨ-permutable) subgroup of G if there exists some x ∈ C such that H^xG_p = G_pH^x, for all G_p ∈ ℨ. We investigate the structure of the finite group G under the assumption that certain subgroups of prime power orders of G are C-ℨ-permutable (conjugate-ℨ-permutable) subgroups of G. Our results improve and generalize several results in the literature.

Keywords:

AMSC: 20D10, 20D15, 20D20, 20F16

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