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].
CITATION STYLE
Borovik, A. V., Lubotzky, A., & Myasnikov, A. G. (2005). The finitary andrews-curtis conjecture. In Progress in Mathematics (Vol. 248, pp. 15–30). Springer Basel. https://doi.org/10.1007/3-7643-7447-0_2
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