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On Certain Torsion Groups Saturated with Finite Simple Groups

A. K. Shlepkin

Krasnoyarsk State Technical University

Abstract: A group $G$ is said to be saturated with groups in a set $X$ provided that every finite subgroup $K\leqslant G$ can be embedded in $G$ into a subgroup $L$ isomorphic to a group in $X$.
It is shown that a torsion group with a finite dihedral Sylow 2-subgroup which is saturated with finite simple nonabelian groups is locally finite and isomorphic to $L_2(P)$ (Theorem 1.1).
It is proven that a torsion group saturated with finite Ree groups is locally finite and isomorphic to a Ree group (Theorem 1.2).

Key words: torsion group, Sylow 2-subgroup, Ree group.

UDC: 512.544

Received: 01.04.1998

 English version: Siberian Advances in Mathematics, 1999, 9:2, 100–108

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