On groups with a strongly embedded unitary subgroup

A. I. Sozutov

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1128-1136

Résumé

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 $U_3(Q)$.

Détail

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