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The Finitary Andrews-Curtis Conjecture

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arxiv 1103.1295 v1 pith:UR2Z7QO2 submitted 2011-03-07 math.GR

Alexandre V. Borovik , Alexander Lubotzky , Alexei G. Myasnikov This is my paper
classification math.GR
keywords finiteandrews-curtisconjecturegroupsversionaskedcannotclassical
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The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexample to the classical conjecture, as suggested in [5].

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  1. Machine-checkable equivalence certificates at the length-14 Andrews-Curtis frontier

    math.GR 2026-07 accept novelty 7.0 of 10

    Explicit elementary-move certificates prove two MS(3) presentations AC-equivalent to AK(3) and realize the automorphism σ on the two remaining open MS(2) classes at length 14.

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