Geodesic
A condition for a finite group to be a Schmidt group
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 81-86

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Let $G$ be a finite group $G$, and let $\pi$ be a set of primes such that $2\in \pi$. We prove that if all maximal subgroups of $G$ are $\pi$-closed and $G$ itself is not $\pi$-closed then $G$ is a Schmidt group. The proof employs the author's earlier results on the properties of pairs $(G,\pi)$ where $G$ is a simple minimal non-$\pi$-closed group and $\pi$ is arbitrary.
Keywords: finite group, Schmidt group, $\pi$-closed group, maximal subgroup.
Mots-clés : simple group 
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     author = {V. A. Belonogov},
     title = {A condition for a finite group to be a {Schmidt} group},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {81--86},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a7/}
}
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V. A. Belonogov. A condition for a finite group to be a Schmidt group. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 81-86. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a7/