RUS  ENG
Full version
JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

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.

UDC: 512.54

MSC: 20E42

Received December 23, 2019, published August 21, 2020

Language: English

DOI: 10.33048/semi.2020.17.085



Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025