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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
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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 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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John Crisp, Luis Paris. 2001-01-30. The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group. https://doi.org/10.1007/s002220100138

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