Bulletin of the London Mathematical Society



Papers

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


O. BOGOPOLSKI a1, A. MARTINO a2, O. MASLAKOVA a3 and E. VENTURA a4
a1 Inst. of Math. of the Sib. Branch of Russian Acad. of Sciences, Novosibirsk, Russia groups@math.nsc.ru
a2 Centre de Recerca Matemàtica, Bellaterra, Spain, Armando.Martino@upc.edu
a3 Inst. of Math. of the Sib. Branch of Russian Acad. of Sciences, Novosibirsk, Russia tessae@ngs.ru
a4 Dept. Mat. Apl. III, UPC, Barcelona, Spain and Dept. of Mathematics, Univ. of Nebraska-Lincoln, enric.ventura@upc.edu

Article author query
bogopolski o   [Google Scholar] 
martino a   [Google Scholar] 
maslakova o   [Google Scholar] 
ventura e   [Google Scholar] 
 

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.

(Received May 6 2004)
(Revised August 2 2005)

Maths Classification

20F10; 20E05.