Groups saturated with finite simple groups $L_3(2^n)$ and $L_4(2^l)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 2, pp. 249-257
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Let $\mathfrak{M}$ be a certain set of groups. For a group $G$, we denote by $\mathfrak{M}(G)$ the set of all subgroups of $G$ that are isomorphic to elements of $\mathfrak{M}$. A group $G$ is said to be saturated with groups from $\mathfrak{M}$ if any finite subgroup of $G$ is contained in some element of $\mathfrak{M}(G)$. We prove that if $G$ is a periodic group or a Shunkov group and $G$ is saturated with groups from the set $\{L_3(2^n), L_4(2^l)\mid n=1,2,\ldots; l=1,\ldots, l_0\},$ where $l_0$ is fixed, then the set of elements of finite order from $G$ forms a group isomorphic to one of the groups from the set $\{L_3 (R), L_4(2^l)\mid l=1,\ldots, l\}$, where $R$ is an appropriate locally finite field of characteristic $2$.
Keywords:
periodic group, Shunkov group, saturation of a group with a set of groups.
@article{TIMM_2022_28_2_a18,
author = {A. A. Shlepkin},
title = {Groups saturated with finite simple groups $L_3(2^n)$ and $L_4(2^l)$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {249--257},
publisher = {mathdoc},
volume = {28},
number = {2},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a18/}
}
A. A. Shlepkin. Groups saturated with finite simple groups $L_3(2^n)$ and $L_4(2^l)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 2, pp. 249-257. http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a18/