Universal diagram groups with identical Poincaré series

Pride, S. (2010) Universal diagram groups with identical Poincaré series. Groups, Geometry and Dynamics, 4(4), pp. 901-908. (doi: 10.4171/GGD/113)

Abstract

For a diagram group G, the first derived quotient G(1)/G(2) is always free abelian (as proved by M. Sapir and V. Guba). However the second derived quotient G(2)/G(3) 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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Pride, Professor Stephen
• Authors: Pride, S.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Groups, Geometry and Dynamics
• ISSN: 1661-7207