The Finitary Andrews-Curtis Conjecture

Details The Finitary Andrews-Curtis Conjecture The Finitary Andrews-Curtis Conjecture

2011-03-07

arxiv.org/abs/1103.1295v1

Mathematics

Group Theory

Appeared in Progress in Mathematics, Vol. 248, 15-30. 2005 Birkh\"auser Verlag Basel/Switzerland

Scientific paper

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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