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

2003/04/21 by Alexei D. Miasnikov, Alexei G. Myasnikov
Mathematics · Computer Science · #math.GR #cs.SC #msc:20E05 #msc:20F05 #msc:68T05 #msc:57M05 #msc:57M20.

paper · pdf

published as In W.Kantor and A.Seress,editors, Groups and Computation III, volume 23, (2001) 257-263, Berlin · 7 pages, no figures

arxiv created 2003/04/21 · arxiv updated 2009/11/30

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.

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