%0 Journal Article
%T Influence of complemented subgroups on the structure of finite groups
%J International Journal of Group Theory
%I University of Isfahan
%Z 2251-7650
%A Malinowska, Izabela Agata
%D 2021
%\ 06/01/2021
%V 10
%N 2
%P 65-74
%! Influence of complemented subgroups on the structure of finite groups
%K Complemented subgroups
%K Complemented groups
%K Minimal non-complemented groups
%K Finite groups
%R 10.22108/ijgt.2019.119105.1570
%X P. Hall proved that a finite group $G$ is supersoluble with elementary abelian Sylow subgroups if and only if every subgroup of $G$ is complemented in $G$. He called such groups complemented. A. Ballester-Bolinches and X. Guo established the structure of minimal non-complemented groups. We give the classification of finite non-soluble groups all of whose second maximal subgroups are complemented groups. We also prove that every finite group with less than $21$ non-complemented non-minimal $\{2,3,5\}$-subgroups is soluble.
%U https://ijgt.ui.ac.ir/article_24261_26abaf2b4bf9f112a26c308aa371615b.pdf