Periodic Groups Saturated with Finite Simple Groups of Lie Type of Rank 1

Abstract

A group G is saturated with groups from a set ℜ of groups if every finite subgroup of G is contained in a subgroup of G that is isomorphic to some group in ℜ. Previously [Kourovka Notebook, Quest. 14.101], the question was posed whether a periodic group saturated with finite simple groups of Lie type whose ranks are bounded in totality is itself a simple group of Lie type. A partial answer to this question is given for groups of Lie type of rank 1. We prove the following: Let a periodic group G be saturated with finite simple groups of Lie type of rank 1. Then G is isomorphic to a simple group of Lie type of rank 1 over a suitable locally finite field.