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.
Cite
@article{arxiv.1711.08091,
title = {Effective Subgroup Separability of Finitely Generated Nilpotent Groups},
author = {Jonas Deré and Mark Pengitore},
journal= {arXiv preprint arXiv:1711.08091},
year = {2018}
}
Comments
V2: Removed reference to erroneous result about effective residual finiteness for nilpotent groups. This has no effect on the methods of the paper, but slightly changes the second part of Theorem 1.1