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
Received March 1, 2019
Revised October 23, 2019
Accepted November 4, 2019
Funding Agency: This work was supported by the Russian Science Foundation (project no. 18-71-10007).
Aleksei Anatolievich Shlepkin, Cand. Phys.-Math. Sci., Institute of Space and Information Technologies of the Siberian Federal University, Krasnoyarsk, 620990 Russia, e-mail: shlyopkin@gmail.com
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Cite this article as: A.A.Shlepkin. On Sylow 2-subgroups of Shunkov groups saturated with the groups $L_3(2^m)$, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 4, pp. 274–281.
