The conjugacy separability growth conjecture for nilpotent groups

Let $N$ be an

-group of nilpotency class $c>1$. Here

denotes the class of groups used in the paper, and $_N(n)$ is the conjugacy separability function of $N$; the relation $f(n)\approx g(n)$ means that $f$ and $g$ are asymptotically equivalent in the paper's sense.

Conjugacy separability growth conjecture.

$$\operatorname{Conj}_N(n)\approx n^{\Phi(N)(c-1)}.$$

The conjecture proposes the general form of the conjugacy separability function for finitely generated nilpotent groups. The lower bound was claimed previously, but the cited argument contains a gap; all known examples satisfy the proposed bounds, and it remains open in general.