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- Title
The generalized conjugacy problem for virtually free groups.
- Authors
Ladra, Manuel; Silva, Pedro V.
- Abstract
The generalized conjugacy problem (has g a conjugate in K for K rational?) is solved for finitely generated (f.g.) virtually free groups with constraints that go beyond the context-free level, a new result for the free group itself. Moldavanskii's theorem on simultaneous conjugacy of f.g. subgroups of a free group is also generalized for virtually free groups and this wider class of constraints. The solution set of the equation x--1 g φφ( x) ∈∈ K in the free group ( φφ a virtually inner automorphism, K rational) is shown to be rational and effectively constructible, and a similar result is proved for the equation xgx--1 ∈∈ K in a f.g. virtually free group. The twisted conjugacy problem with context-free constraints is also proved to be decidable for the free group.
- Subjects
FREE groups; AUTOMORPHISMS; SET theory; MACHINE theory; NUMERICAL solutions to equations; MATHEMATICAL transformations; MATHEMATICAL proofs
- Publication
Forum Mathematicum, 2011, Vol 23, Issue 3, p447
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/FORM.2011.015