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].
To Slava Grigorchuk as a token of our friendship.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Borovik, A.V., Lubotzky, A., Myasnikov, A.G. (2005). The Finitary Andrews-Curtis Conjecture. In: Bartholdi, L., Ceccherini-Silberstein, T., Smirnova-Nagnibeda, T., Zuk, A. (eds) Infinite Groups: Geometric, Combinatorial and Dynamical Aspects. Progress in Mathematics, vol 248. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7447-0_2
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