The conjugacy problem is solvable in free-by-cyclic groups

被引：36
|
作者：
Bogopolski, O. [1 ]
Martino, A.
Maslakova, O.
Ventura, E.
机构：
[1] Russian Acad Sci, Inst Math, Sib Branch, Novosibirsk 630090, Russia
[2] Ctr Recerca Matemat, Bellaterra, Spain
[3] UPC, Dept Mat Apl 3, Barcelona, Spain
[4] Univ Nebraska, Dept Math, Lincoln, NE USA
来源：
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2006年 / 38卷
关键词：
D O I：
10.1112/S0024609306018674
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：787 / 794
页数：8
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