The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group
John Crisp, Luis Paris
Abstract
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 a2 and b2 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 sm(s) of the generators are that am(a) and bm(b) commute if ab=ba appears amongst the Artin relations.
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