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 \cite{bogopolski2006conjugacy} and Bogopolski, Martino, and Ventura in \cite{bogopolski2010orbit}, to free abelian-by-infinite cyclic groups, and in certain cases apply a polynomial time algorithm for the orbit problem over $\Z^n$ by Kannan and Lipton.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.5297
- arXiv:
- arXiv:1410.5297
- Bibcode:
- 2014arXiv1410.5297C
- Keywords:
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- Mathematics - Group Theory;
- Computer Science - Computational Complexity