The Center of Thin Gaussian Groups

Thin Gaussian groups are a natural generalization of spherical Artin groups, namely groups of fractions of monoids in which the existence of least common multiples is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be of Coxeter type. Here we completely describe the center of thin Gaussian groups by constructing a minimal generating set for the quasi-center. We deduce that every thin Gaussian group is an iterated crossed product of thin Gaussian groups with a cyclic center.