4 problems

Center conjecture. The center of every irreducible Artin group of infinite type is trivial:

Let $A_\Gamma$ be an Artin group with irreducible factor decomposition … A factor $A_{\Gamma_i}$ is spherical when its associated Coxeter group is finite. The center conjecture. Th…

Conjecture. All finite abelian groups are completely $L$-realisable.

Let $W$ be an irreducible finite complex reflection group, with pure braid group $P$ and braid group $B$. Let $Z(P)$ and $Z(B)$ denote their centers, and let … be the natural eleme…