6533b827fe1ef96bd128669e

RESEARCH PRODUCT

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

Luis ParisJohn Crisp

subject

CombinatoricsMathematics::Group TheoryConjectureGeneral MathematicsMathematics::Rings and AlgebrasFOS: MathematicsGenerating set of a groupArtin group20F36 (Primary) 57N05 (Secondary)Group Theory (math.GR)Mathematics - Group TheoryMathematics

description

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.

yearjournalcountryeditionlanguage
2000-03-22
10.1007/s002220100138http://arxiv.org/abs/math/0003133