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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.
Received December 23, 2019, published August 21, 2020
Citation:
A. I. Sozutov, “On groups with a strongly embedded unitary subgroup”, Sib. Èlektron. Mat. Izv., 17 (2020), 1128–1136
Linking options:
https://www.mathnet.ru/eng/semr1279 https://www.mathnet.ru/eng/semr/v17/p1128
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