Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture
Group Theory
2007-05-23 v1 Symbolic Computation
Abstract
The Andrews-Curtis conjecture states that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of the elementary Nielsen transformations and conjugations. In this paper we describe all balanced presentations of the trivial group on two generators and with the total length of relators <= 12. We show that all these presentations satisfy the Andrews-Curtis conjecture.
Keywords
Cite
@article{arxiv.math/0304305,
title = {Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture},
author = {Alexei D. Miasnikov and Alexei G. Myasnikov},
journal= {arXiv preprint arXiv:math/0304305},
year = {2007}
}
Comments
7 pages, no figures