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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67169The 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.7 pages, no figuresGroup TheorySymbolic Computation20E05, 20F05, 68T05 (Primary), 57M05,57M20. (Secondary)Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecturetext