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.
We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd and even .
In the present article we define W-paths of elements in a W-perfect group as a useful tools and obtain their basic properties.