Some commutativity criteria. - II
A subgroup of a group is said to be normal-by-finite if the core of in has finite index in . It has been proved by Buckley, Lennox, Neumann, Smith and Wiegold that if every subgroup of a group G is normal-by-finite, then is abelian-by-finite, provided that all its periodic homomorphic images are locally finite. The aim of this article is to describe the structure of groups G for which the partially ordered set consisting of all normal-by-finite subgroups satisfies certain relevant...
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.
Let be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in as those intersecting only Bruhat cells in corresponding to involutions in the Weyl group of .
We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.