Shunkov groups saturated with almost simple groups
Algebra i logika, Tome 62 (2023) no. 1, pp. 93-101
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A group $G$ is called a Shunkov group (a conjugate biprimitive finite group) if, for any of its finite subgroups $H$ in the factor group $N_G(H)/H$, every two conjugate elements of prime order generate a finite subgroup. We say that a group is saturated with groups from the set $\mathfrak{M}$ if any finite subgroup of the given group is contained in its subgroup isomorphic to some group in $\mathfrak{M}$. We show that a Shunkov group $G$ which is saturated with groups from the set $\mathfrak{M}$ possessing specific properties, and contains an involution $z$ with the property that the centralizer $C_G(z)$ has only finitely many elements of finite order will have a periodic part isomorphic to one of the groups in $\mathfrak{M}$. In particular, a Shunkov group $G$ that is saturated with finite almost simple groups and contains an involution $z$ with the property that the centralizer $C_G(z)$ has only finitely many elements of finite order will have a periodic part isomorphic to a finite almost simple group.
Keywords:
Shunkov group, saturated set, almost simple group.
@article{AL_2023_62_1_a6,
author = {N. V. Maslova and A. A. Shlepkin},
title = {Shunkov groups saturated with almost simple groups},
journal = {Algebra i logika},
pages = {93--101},
publisher = {mathdoc},
volume = {62},
number = {1},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AL_2023_62_1_a6/}
}
N. V. Maslova; A. A. Shlepkin. Shunkov groups saturated with almost simple groups. Algebra i logika, Tome 62 (2023) no. 1, pp. 93-101. http://geodesic.mathdoc.fr/item/AL_2023_62_1_a6/