Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture

Details Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture

2003-04-21

arxiv.org/abs/math/0304305v1

In W.Kantor and A.Seress,editors, Groups and Computation III, volume 23, (2001) 257-263, Berlin

Mathematics

Group Theory

7 pages, no figures

Scientific paper

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.

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