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The number of conjugacy classes in pattern groups is not a polynomial function
-
Zoltán Halasi
and
Péter P. Pálfy
Published/Copyright:
March 15, 2011
Abstract
A famous open problem due to Graham Higman asks if the number of conjugacy classes in the group of n × n unipotent upper triangular matrices over the q-element field can be expressed as a polynomial function of q for every fixed n. We consider the generalization of the problem for pattern groups and prove that for some pattern groups of nilpotency class two the number of conjugacy classes is not a polynomial function of q.
Received: 2010-08-18
Revised: 2010-11-22
Published Online: 2011-03-15
Published in Print: 2011-November
© de Gruyter 2011
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Articles in the same Issue
- Remarks on chains of weakly closed subgroups
- Closed normal subgroups of free pro-S-groups of finite rank
- Point stabilisers for the enhanced and exotic nilpotent cones
- The number of conjugacy classes in pattern groups is not a polynomial function
- On finite T-groups and the Wielandt subgroup
- A direct product coming from a particular set of character degrees
- Centralizers in Ã2 groups
- On centralizers of parabolic subgroups in Coxeter groups
- Local splitting of locally compact groups and pro-Lie groups
- Cylindric embeddings of Cayley graphs
- Compactifications of a representation variety
