Universal diagram groups with identical Poincare series
Steve Pride (U Glasgow)
Wednesday 26th January, 2011 16:00-17:00 204
For a diagram group G, the first derived quotient G1/G2 is always free abelian (as proved by M. Sapir and V. Guba). However the second derived quotient G2/G3 may contain torsion. In fact, we show that for any finite or countably infinite direct product of cyclic groups A, there is a diagram group with second derived quotient A. We use that to construct families with the properties of the title.