an:05152176
Zbl 1114.20011
Borovik, Alexandre V.; Lubotzky, Alexander; Myasnikov, Alexei G.
The finitary Andrews-Curtis conjecture.
EN
Bartholdi, Laurent (ed.) et al., Infinite groups: geometric, combinatorial and dynamical aspects. Based on the international conference on group theory: geometric, combinatorial and dynamical aspects of infinite groups, Gaeta, Italy, June 1--6, 2003. Basel: BirkhĂ¤user (ISBN 3-7643-7446-2/hbk). Progress in Mathematics 248, 15-30 (2005).
2005
a
20E05 20F05
Andrews-Curtis conjecture; connected components of Andrews-Curtis graphs of finite groups; computation in finite groups
Summary: The well known Andrews-Curtis conjecture [\textit{J. J. Andrews} and \textit{M. L. Curtis}, Proc. Am. Math. Soc. 16, 192-195 (1965; Zbl 0131.38301)] 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 by \textit{A. V. Borovik, E. I. Khukhro} and \textit{A. G. Myasnikov} [in Int. J. Algebra Comput. 13, No. 4, 415-436 (2003; Zbl 1053.20023)] and shows that a computation in finite groups cannot lead to a counterexample to the classical conjecture, as suggested in [loc. cit.].
For the entire collection see [Zbl 1083.20500].
0131.38301; 1053.20023