Open AccessOn -permutable subgroups in finite groups
Author(s) -
Bin Hu,
Jianhong Huang,
N. M. Adarchenko
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i10.768
Subject(s) - permutable prime , mathematics , partition (number theory) , separable space , combinatorics , set (abstract data type) , group (periodic table) , discrete mathematics , physics , mathematical analysis , computer science , quantum mechanics , programming language
UDC 512.542Let be some partition of the set of all primes and let be a nonempty subset of the set A set of subgroups of a finite group is said to be a \emph{complete Hall -set} of if every member of is a Hall -subgroup of for some and contains exactly one Hall -subgroup of for every such that A subgroup of is called (i) {- permutable } if for and ; (ii) {- permutable in } if is -permutable for some complete Hall -set of We study the influence of -permutable subgroups on the structure of In particular, we prove that if and where and are -permutable -separable (respectively, -closed) subgroups of then is also -separable (respectively, -closed). Some known results are generalized.