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.
Malinowska, I. (2021). Influence of complemented subgroups on the structure of finite groups. International Journal of Group Theory, 10(2), 65-74. doi: 10.22108/ijgt.2019.119105.1570
MLA
Izabela Agata Malinowska. "Influence of complemented subgroups on the structure of finite groups". International Journal of Group Theory, 10, 2, 2021, 65-74. doi: 10.22108/ijgt.2019.119105.1570
HARVARD
Malinowska, I. (2021). 'Influence of complemented subgroups on the structure of finite groups', International Journal of Group Theory, 10(2), pp. 65-74. doi: 10.22108/ijgt.2019.119105.1570
VANCOUVER
Malinowska, I. Influence of complemented subgroups on the structure of finite groups. International Journal of Group Theory, 2021; 10(2): 65-74. doi: 10.22108/ijgt.2019.119105.1570
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