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Influence of complemented subgroups on the structure of finite groups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 10، شماره 2، شهریور 2021، صفحه 65-74 اصل مقاله (206.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2019.119105.1570 | ||
| نویسنده | ||
| Izabela Agata Malinowska* | ||
| Faculty of Mathematics, University of Bialystok, 15-245 Bialystok, Ciolkowskiego 1M, Poland | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Complemented subgroups؛ Complemented groups؛ Minimal non-complemented groups؛ Finite groups | ||
| مراجع | ||
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