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Some lattice properties of normal-by-finite subgroups

Maria De Falco, Carmela Musella (2003)

Bollettino dell'Unione Matematica Italiana

A subgroup H of a group G is said to be normal-by-finite if the core H G of H in G has finite index in H . It has been proved by Buckley, Lennox, Neumann, Smith and Wiegold that if every subgroup of a group G is normal-by-finite, then G 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 nf G consisting of all normal-by-finite subgroups satisfies certain relevant...

Some remarks on groups in which elements with the same p -power commute

Patrizia Longobardi, Mercede Maj (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we characterize certain classes of groups G in which, from x p = y p ( x , y G , p a fixed prime), it follows that x y = y x . Our results extend results previously obtained by other authors, in the finite case.

Spherical conjugacy classes and the Bruhat decomposition

Giovanna Carnovale (2009)

Annales de l’institut Fourier

Let G be a connected, reductive algebraic group over an algebraically closed field of zero or good and odd characteristic. We characterize spherical conjugacy classes in G as those intersecting only Bruhat cells in G corresponding to involutions in the Weyl group of  G .

Spherical functions and uniformly bounded representations of free groups

Tadeusz Pytlik (1991)

Studia Mathematica

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.

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