Effective separability of finitely generated nilpotent groups

摘要

We give effective proofs of residual finiteness and conjugacy separability for finitely generated nilpotent groups. In particular, we give precise effective bounds for a function introduced by Bou-Rabee that measures how large the finite quotients that are needed to separate nonidentity elements of bounded length from the identity which improves the work of Bou-Rabee. Similarly, we give polynomial upper and lower bounds for an analogous function introduced by Lawton, Louder, and McReynolds that measures how large the finite quotients that are needed to separate pairs of distinct conjugacy classes of bounded word length using work of Blackburn and Mal'tsev.