Title: Effective Subgroup Separability of Finitely Generated Nilpotent Groups,
Abstract: This paper studies effective separability for subgroups of finitely generated
nilpotent groups and more broadly effective subgroup separability of finitely
generated nilpotent groups. We provide upper and lower bounds that are
polynomial with respect to the logarithm of the word length for infinite index
subgroups of nilpotent groups. In the case of normal subgroups, we provide an
exact computation generalizing work of the second author. We introduce a
function that quantifies subgroup separability, and we provide polynomial upper
and lower bounds. We finish by demonstrating that our results extend to
virtually nilpotent groups.