A Polynomial Time Algorithm For The Conjugacy Decision and Search Problems in Free Abelian-by-Infinite Cyclic Groups
Abstract
In this paper we introduce a polynomial time algorithm that solves both the conjugacy decision and search problems in free abelian-by-infinite cyclic groups where the input is elements in normal form. We do this by adapting the work of Bogopolski, Martino, Maslakova, and Ventura in bogopolski2006conjugacy and Bogopolski, Martino, and Ventura in bogopolski2010orbit, to free abelian-by-infinite cyclic groups, and in certain cases apply a polynomial time algorithm for the orbit problem over n by Kannan and Lipton.
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