4 papers
Parabolic subgroups of Dyer groups
María Cumplido, Marina Salamero, Giovanni Sartori +1
For all Dyer groups, we find an algorithm to determine when two parabolic subgroups are conjugate. Given two conjugate standard parabolic subgroup, we fully describe the conjugatin…
Isomorphism invariance of the girth of Artin groups
Giovanni Sartori
For all Artin groups, we characterise the girth (i.e. the length of a shortest cycle) of the defining graph algebraically, showing that it is an isomorphism invariant. Using this r…
A combination theorem for the twist conjecture for Artin groups
Oli Jones, Giorgio Mangioni, Giovanni Sartori
We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups sa…
JSJ splittings for all Artin groups
Oli Jones, Giorgio Mangioni, Giovanni Sartori
We prove that an Artin group splits over infinite cyclic subgroups if and only if its defining graph has a separating vertex, and explicitly construct a JSJ decomposition over infi…