Menachem Shlossberg (University of Udine)
Algebraic entropy in compactly covered locally compact groups

A topological group G is called compactly covered if each element of G is contained in some compact subgroup of G. We study the algebraic entropy in compactly covered locally compact groups (cclc for short) that satisfy certain cofinality conditions. Two important subclasses which we consider are:

1)Compactly covered locally compact abelian groups. This subclass contains for example all compact abelian groups, all LCA torsion groups and the p-adic numbers Q_p.

2)Discrete locally finite and normal groups. A  group G is called locally finite and normal if each finite subset F is contained in a finite normal subgroup N of G.  Among these groups are direct sums of finite groups, their subgroups, and quotient groups. The Hamiltonian groups, that is, the non-abelian groups in which every subgroup is normal are also locally finite and normal.

This is a joint work (in progress) with Anna Giordano Bruno and Daniele Toller.