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THE CONJUGACY PROBLEM IS SOLVABLE IN FREE-BY-CYCLIC GROUPS

Published online by Cambridge University Press:  20 September 2006

O. BOGOPOLSKI ,
A. MARTINO ,
O. MASLAKOVA  and
E. VENTURA
O. BOGOPOLSKI
Affiliation:
Inst. of Math. of the Sib. Branch of Russian Acad. of Sciences, Novosibirsk, Russiagroups@math.nsc.ru
A. MARTINO
Affiliation:
Centre de Recerca Matemàtica, Bellaterra, Spain, Armando.Martino@upc.edu
O. MASLAKOVA
Affiliation:
Inst. of Math. of the Sib. Branch of Russian Acad. of Sciences, Novosibirsk, Russiatessae@ngs.ru
E. VENTURA
Affiliation:
Dept. Mat. Apl. III, UPC, Barcelona, Spain and Dept. of Mathematics, Univ. of Nebraska-Lincoln, enric.ventura@upc.edu
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Abstract

We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one of P. Brinkmann that one can determine whether two cyclic words in a free group are mapped to each other by some power of a given automorphism. We also solve the power conjugacy problem, and give an algorithm to recognize whether two given elements of a finitely generated free group are twisted conjugated to each other with respect to a given automorphism.

Keywords

20F1020E05
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 5 , October 2006 , pp. 787 - 794
Copyright
© The London Mathematical Society 2006

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