Geodesic
Finite Groups with Three Nonconjugate Maximal Formational Subgroups
Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 354-364

Voir la notice de l'article provenant de la source Math-Net.Ru

A constructive description is obtained for the hereditary $Z$-saturated formations $\mathfrak{F}$ of finite solvable groups containing every solvable group possessing three pairwise nonconjugate maximal subgroups belonging to $\mathfrak{F}$. It is proved that a finite group $G$ is supersolvable if it has three pairwise nonconjugate supersolvable maximal subgroups and its commutator subgroup $G'$ is nilpotent.
Keywords: finite group, maximal subgroup, $Z$-saturated formation, formation with the Belonogov property, formation with the Kegel property
Mots-clés : supersolvable group. 
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     author = {A. F. Vasil'ev and V. I. Murashka and A. K. Furs},
     title = {Finite {Groups} with {Three} {Nonconjugate} {Maximal} {Formational} {Subgroups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {354--364},
     publisher = {mathdoc},
     volume = {111},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a2/}
}
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A. F. Vasil'ev; V. I. Murashka; A. K. Furs. Finite Groups with Three Nonconjugate Maximal Formational Subgroups. Matematičeskie zametki, Tome 111 (2022) no. 3, pp. 354-364. http://geodesic.mathdoc.fr/item/MZM_2022_111_3_a2/