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The Conjugacy Problem is Solvable in Free‐By‐Cyclic Groups
Author(s) -
Bogopolski O.,
Martino A.,
Maslakova O.,
Ventura E.
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018674
Subject(s) - mathematics , conjugacy problem , conjugacy class , automorphism , finitely generated abelian group , cyclic group , group (periodic table) , combinatorics , outer automorphism group , free group , automorphism group , pure mathematics , discrete mathematics , abelian group , chemistry , organic chemistry
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. 2000 Mathematics Subject Classification 20F10, 20E05.