TY - CHAP
T1 - The finitary andrews-curtis conjecture
AU - Borovik, Alexandre V.
AU - Lubotzky, Alexander
AU - Myasnikov, Alexei G.
N1 - Publisher Copyright:
© 2005, Birkhäuser Verlag Basel/Switzerland.
PY - 2005
Y1 - 2005
N2 - 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].
AB - 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].
KW - Andrews-Curtis conjecture
KW - Finite group
KW - Generators
UR - http://www.scopus.com/inward/record.url?scp=84954310977&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84954310977&partnerID=8YFLogxK
U2 - 10.1007/3-7643-7447-0_2
DO - 10.1007/3-7643-7447-0_2
M3 - Chapter
AN - SCOPUS:84954310977
T3 - Progress in Mathematics
SP - 15
EP - 30
BT - Progress in Mathematics
ER -