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 Sib. Èlektron. Mat. Izv., 2020, Volume 17, Pages 1128–1136 (Mi semr1279)

Mathematical logic, algebra and number theory

On groups with a strongly embedded unitary subgroup

A. I. Sozutov

Siberian Federal University, 79, Svobodny ave., Krasnoyarsk, 660041, Russia

Abstract: A proper subgroup $B$ of a group $G$ is called strongly embedded, if $2\in\pi(B)$ and $2\notin\pi(B \cap B^g)$ for every element $g \in G \setminus B$, and therefore $N_G(X) \leq B$ for every $2$-subgroup $X \leq B$. An element $a$ of a group $G$ is called finite, if for every $g\in G$ the subgroup $\langle a, a^g \rangle$ is finite.
In the paper, it is proved that a group with a finite element of order $4$ and a strongly embedded subgroup isomorphic to the Borel subgroup of $U_3(Q)$ over a locally finite field $Q$ of characteristic $2$ is locally finite and isomorphic to the group $U_3(Q)$.

Keywords: A strongly embedded subgroup of a unitary type, Borel subgroup, Cartan subgroup, involution, finite element.

 Funding Agency Grant Number Russian Science Foundation 19-71-10017 This work is supported by the Russian Science Foundation under grant No. 19-71-10017.

DOI: https://doi.org/10.33048/semi.2020.17.085

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Bibliographic databases:

UDC: 512.54
MSC: 20E42
Received December 23, 2019, published August 21, 2020
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Citation: A. I. Sozutov, “On groups with a strongly embedded unitary subgroup”, Sib. Èlektron. Mat. Izv., 17 (2020), 1128–1136

Citation in format AMSBIB
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