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

Alexei D. Miasnikov; Alexei G. Myasnikov

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

Alexei D. Miasnikov·Alexei G. Myasnikov

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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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BibTeX RIS

Alexei D. Miasnikov, Alexei G. Myasnikov. 2003-04-21. Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture. https://arxiv.org/abs/math/0304305

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