On Sylow 2-subgroups of Shunkov groups saturated with the groups $L_3(2^m)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 4, pp. 275-282
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A group $G$ is saturated with groups from a set of groups $X$ if any finite subgroup of $G$ is contained in a subgroup of $G$ isomorphic to some group from $X$. If all finite-order elements of a group $G$ are contained in a periodic subgroup of $G$, then this subgroup is called the periodic part of $G$. A group $G$ is called a Shunkov group if, for any finite subgroup $H$ of $G$, any two conjugate elements of prime order in the quotient group $N_G(H)/h$ generate a finite group. A Shunkov group may have no periodic part. We establish the structure of a Sylow 2-subgroup of a Shunkov group saturated with projective special linear groups of degree 3 over finite fields of even characteristic in the case when the Shunkov group has no periodic part.
Keywords:
group saturated with a given set of groups, Shunkov group, periodic part of a group.
@article{TIMM_2019_25_4_a28,
author = {A. A. Shlepkin},
title = {On {Sylow} 2-subgroups of {Shunkov} groups saturated with the groups $L_3(2^m)$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {275--282},
publisher = {mathdoc},
volume = {25},
number = {4},
year = {2019},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a28/}
}
TY - JOUR AU - A. A. Shlepkin TI - On Sylow 2-subgroups of Shunkov groups saturated with the groups $L_3(2^m)$ JO - Trudy Instituta matematiki i mehaniki PY - 2019 SP - 275 EP - 282 VL - 25 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a28/ LA - ru ID - TIMM_2019_25_4_a28 ER -
A. A. Shlepkin. On Sylow 2-subgroups of Shunkov groups saturated with the groups $L_3(2^m)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 25 (2019) no. 4, pp. 275-282. http://geodesic.mathdoc.fr/item/TIMM_2019_25_4_a28/