Open AccessFinite Groups with Certain Permutability Criteria
Author(s) -
Rola Hijazi,
Fatme M. Charaf
Publication year - 2019
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.v12i2.3399
Subject(s) - mathematics , permutable prime , sylow theorems , complement (music) , combinatorics , nilpotent , finite group , index of a subgroup , group (periodic table) , subgroup , discrete mathematics , biochemistry , chemistry , organic chemistry , complementation , gene , phenotype
Let G be a finite group. A subgroup H of G is said to be S-permutable in G if itpermutes with all Sylow subgroups of G. In this note we prove that if P, the Sylowp-subgroup of G (p > 2), has a subgroup D such that 1 <|D|<|P| and all subgroups H of P with |H| = |D| are S-permutable in G, then G′ is p-nilpotent.