School Seminars and Colloquia

Finiteness conditions for subdirect products of groups

Geometry/Topology Seminar

by Professor Chuck Miller


Institution: University of Melbourne
Date: Mon 11th April 2005
Time: 3:15 PM
Location: Room 213, Richard Berry Building, University of Melbourne

Abstract: A subgroup G of a direct product of groups is called
a subdirect product if the projections map G surjectively onto
the factors. A subdirect product of two groups is the same as
a pull-back or fibre product of two homomorphisms from the
factors onto the same quotient group. An old result of Mihailova
is that the direct product of two free groups has finitely
generated subgroups for which membership is recursively
undecidable. Grunewald showed these subgroups are not
finitely presented, and more generally Baumslag and Roseblade
showed the direct product of two free groups has only the obvious
finitely presented subgroups. In this talk I will report on joint
efforts with a number of colleagues to determine when subdirect
products are finitely presented and what other finiteness and
homological properties they enjoy. Many algorithmic problems for
finitely presented subgroups of direct products of very nice
groups can be unsolvable.

For More Information: Craig Hodgson tel: 8344-5553 email: c.hodgson@ms.unimelb.edu.au