Simple groups with prescribed local structure
In this paper we characterize certain classes of groups in which, from (, a fixed prime), it follows that . Our results extend results previously obtained by other authors, in the finite case.
A group G is strongly bounded if every isometric action of G on a metric space has bounded orbits. We show that the automorphism groups of typical countable structures with the small index property are strongly bounded. In particular we show that this is the case when G is the automorphism group of the countable universal locally finite extension of a periodic abelian group.
A characterization of strict S-partitions in locally finite groups is given.