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Andrews–Curtis groups and the Andrews–Curtis conjecture
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Adam Piggott
Published/Copyright:
June 18, 2007
Abstract
For an integer n at least two and a positive integer m, let 
C(n,m) denote the group of Andrews–Curtis transformations of rank (n,m) and let F denote the free group of rank n + m. A subgroup AC(n,m) of Aut(F) is defined, and an anti-isomorphism AC(n,m) to C(n,m) is described. We solve the generalized word problem for AC(n,m) in Aut(F) and discuss an associated reformulation of the Andrews–Curtis conjecture.
Received: 2006-02-28
Revised: 2006-07-24
Published Online: 2007-06-18
Published in Print: 2007-05-23
© Walter de Gruyter
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Articles in the same Issue
- Transitivity properties for group actions on buildings
- Fields, values and character extensions in finite groups
- Primitive sharp permutation groups with large solvable subgroups
- On the size of the nilpotent residual in finite groups
- On the commuting complex of finite metanilpotent groups
- Soluble normally constrained pro-p-groups
- Comparing quasi-finitely axiomatizable and prime groups
- A finitely presented torsion-free simple group
- Andrews–Curtis groups and the Andrews–Curtis conjecture
- Residual finiteness of outer automorphism groups of certain tree products
- Commutator subgroups of Hantzsche–Wendt groups
