Centralizer Dimensions of Partially Commutative Metabelian Groups

Resumo

We establish an upper bound for the centralizer dimension of a partially commutative metabelian group that depends linearly on the number of vertices in a defining graph. It is proved that centralizer dimensions of 2-generated metabelian groups are not bounded above. The exact value of the centralizer dimension is computed for a partially commutative metabelian group defined by a cycle.