Open AccessThe Influence of C- Z-permutable Subgroups on the Structure of Finite Groups
Author(s) -
M. M. Al-Shomrani,
Abdlruhman A. Heliel
Publication year - 2018
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v11i1.3184
Subject(s) - mathematics , permutable prime , sylow theorems , combinatorics , prime (order theory) , order (exchange) , group (periodic table) , locally finite group , complement (music) , finite group , discrete mathematics , physics , biochemistry , abelian group , chemistry , finance , quantum mechanics , complementation , economics , gene , phenotype
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.