DIMACS Tutorial on Exotic Constructions in Group Theory

September 20 - 21, 2010
DIMACS Center, CoRE Building, Rutgers University

Robert Gilman, Stevens, Robert.Gilman at stevens.edu
Bakhodyr Khoussainov, The University of Auckland (New Zealand), bmk at cs.auckland.ac.nz
Alexei Miasnikov, Stevens, amiasnik at stevens.edu


Combinatorial group theory has a long history of computation despite the seemingly paradoxical fact that almost all problems having to do with finitely presented groups are recursively unsolvable. Many decision problems are solvable for automatic groups, word hyperbolic groups, nilpotent groups, and other well known classes. On the other hand, there are constructions of groups, Tarski monsters for example, with bizarre properties. This tutorial is devoted to the question of whether techniques from recursive function theory and model theory (such as forcing and priority arguments) which so far have not been much employed in combinatorial group theory can help to delineate the boundary between well behaved and wild groups by affording methods for constructing groups with desired properties. This question will be explored from a number of different perspectives.

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Document last modified on July 12, 2010.