TY - JOUR
ID - 24261
TI - Influence of complemented subgroups on the structure of finite groups
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Malinowska, Izabela Agata
AD - Faculty of Mathematics, University of Bialystok, 15-245 Bialystok, Ciolkowskiego 1M, Poland
Y1 - 2021
PY - 2021
VL - 10
IS - 2
SP - 65
EP - 74
KW - Complemented subgroups
KW - Complemented groups
KW - Minimal non-complemented groups
KW - Finite groups
DO - 10.22108/ijgt.2019.119105.1570
N2 - 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.
UR - https://ijgt.ui.ac.ir/article_24261.html
L1 - https://ijgt.ui.ac.ir/article_24261_26abaf2b4bf9f112a26c308aa371615b.pdf
ER -