The Finitary Andrews-Curtis Conjecture

2011/03/07 by Alexandre Borovik, Alexander Lubotzky, Borovik, Alexandre V. +3 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1103.1295

openalex publication_date 2011/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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