On a covering group theorem and its applications.
We conjecture that every finite group G acting on a contractible CW-complex X of dimension 2 has at least one fixed point. We prove this in the case where G is solvable, and under this additional hypothesis, the result holds for X acyclic.
As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by whenever T is torsion abelian and L is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of LT is determined by the structure of the localization of the primary components of T in many cases. Furthermore, we completely characterize the relationship...