%0 Journal Article %T The Finitary Andrews-Curtis Conjecture %A Alexandre V. Borovik %A Alexander Lubotzky %A Alexei G. Myasnikov %J Mathematics %D 2011 %I arXiv %X 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]. %U http://arxiv.org/abs/1103.1295v1