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The Conjugacy Problem is Solvable in Free-By-Cyclic Groups |
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| Authors: | Bogopolski, O. Martino, A. Maslakova, O. Ventura, E. |
| Affiliation: | Inst. of Math. of the Sib. Branch of Russian Acad. of Sciences Novosibirsk, Russia groups{at}math.nsc.ru Centre de Recerca Matemàtica Bellaterra, Spain, Armando.Martino{at}upc.edu Inst. of Math. of the Sib. Branch of Russian Acad. of Sciences Novosibirsk, Russia tessae{at}ngs.ru Dept. Mat. Apl. III UPC, Barcelona, Spain and Dept. of Mathematics, Univ. of Nebraska-Lincoln enric.ventura{at}upc.edu |
| Abstract: | We show that the conjugacy problem is solvable in [finitelygenerated free]-by-cyclic groups, by using a result of O. Maslakovathat one can algorithmically find generating sets for the fixedsubgroups of free group automorphisms, and one of P. Brinkmannthat one can determine whether two cyclic words in a free groupare mapped to each other by some power of a given automorphism.We also solve the power conjugacy problem, and give an algorithmto recognize whether two given elements of a finitely generatedfree group are twisted conjugated to each other with respectto a given automorphism. 2000 Mathematics Subject Classification20F10, 20E05. |
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