Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture
<|reference_start|>Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture: 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.<|reference_end|>
@article{miasnikov2003balanced,
    title={Balanced presentations of the trivial group on two generators and the
  Andrews-Curtis conjecture},
    author={Alexei D. Miasnikov, Alexei G. Myasnikov},
    journal={In W.Kantor and A.Seress,editors, Groups and Computation III,
  volume 23, (2001) 257-263, Berlin},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0304305},
    primaryClass={math.GR cs.SC}
}