Local indicability and commutator subgroups of Artin groups
نویسنده
چکیده
Artin groups (also known as Artin-Tits groups) are generalizations of Artin’s braid groups. This paper concerns Artin groups of spherical type, that is, those whose corresponding Coxeter group is finite, as is the case for the braid groups. We compute presentations for the commutator subgroups of the irreducible spherical-type Artin groups, generalizing the work of Gorin and Lin [GL69] on the braid groups. Using these presentations we determine the local indicability of the irreducible spherical Artin groups (except for F4 which at this time remains undetermined). We end with a discussion of the current state of the right-orderability of the spherical-type Artin groups.
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