The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group

Details The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group

2000-03-22

arxiv.org/abs/math/0003133v2

Invent. Math. 145, 19--36 (2001)

Mathematics

Group Theory

18 pages, 11 figures (.eps files generated by pstricks.tex). Prepublication du Laboratoire de Topologie UMR 5584 du CNRS (Univ

Scientific paper

10.1007/s002220100138

It was conjectured by Tits that the only relations amongst the squares of the standard generators of an Artin group are the obvious ones, namely that a^2 and b^2 commute if ab=ba appears as one of the Artin relations. In this paper we prove Tits' conjecture for all Artin groups. More generally, we show that, given a number m(s)>1 for each Artin generator s, the only relations amongst the powers s^m(s) of the generators are that a^m(a) and b^m(b) commute if ab=ba appears amongst the Artin relations.

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