SEMINAR: Groups and Combinatorics Seminar: A duality for mixed abelian groups

Groups and Combinatorics Seminar

Phill Shultz (UWA) will speak on

A duality for mixed abelian groups

at 12 noon on Tuesday 29th of March in MLR2

Abstract: An abelian group is mixed if it contains non-zero elements of finite and of infinite order, and well mixed if it is not the direct sum of a torsion and a torsion-free group. The classification of well mixed groups is an intractable problem.

In this seminar, I will use a duality to describe the structure of well mixed groups G satisfying two finiteness conditions:

1. G has finite rank, that is, G contains a maximal free subgroup of finite dimension;

2. G is self-small, that is, the image of every homomorphism from G into an infinite direct sum of copies of G is contained in the direct sum of finitely many of these copies.

All welcome