On the periodic part of a Shunkov group saturated with linear and unitary groups of degree 3 over finite fields of odd characteristic

A. A. Shlepkin

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 27 (2021) no. 1, pp. 207-219

Résumé

Let $G$ be a group, and let $\mathfrak{X}$ be a set of groups. A group $G$ is saturated with groups from the set $\mathfrak{X}$ if any finite subgroup of $G$ is contained in a subgroup of $G$ isomorphic to some group from $\mathfrak{X}$. If all elements of finite orders from $G$ are contained in a periodic subgroup $T(G)$ of $G$, then $T(G)$ is called the periodic part of $G$. A group $G$ is called a Shunkov group if, for any finite subgroup $H$ of $G$, in $G/N(G)$ any two conjugate elements of prime order generate a finite group. A Shunkov group may have no periodic part. It is proved that a Shunkov group saturated with finite linear and unitary groups of degree 3 over finite fields of characteristic 2 has a periodic part, which is isomorphic to either a linear or a unitary group of degree 3 over a suitable locally finite field of characteristic 2.

Détail

Keywords: groups with saturation conditions, Shunkov group, periodic part of a group.