Estimation of recurrence for nilpotent group action

Abstract

We estimate size of recurrence of an action of a nilpotent group by homeomorphisms of a compact space for polynomial mappings into a nilpotent group form the partial semigroup $({\mathcal{P}}_f(\mathbb{N}),\uplus )$. To do this we have used algebraic structure of the Stone-Čech copactification partial semigroup and that of the given nilpotent group.