Author

Ilya Kapovich

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Preprint Jul 2026

Compressed primitivity problem in free groups

For a fixed integer $r\ge 2$, we prove that the \emph{compressed primitivity problem} in the free group $F_r=F(x_1,\dots,x_r)$ is decidable in non-deterministic polynomial time. That is, for a \emph{straight-line program} $\mathcal A$ over $\{x_1,\dots,x_r\}^{\pm1}$ representing an element $g\in F_r$, the problem of de...

Ilya Kapovich · 0 citations

Preprint Aug 2026

Small Cancellation Stability and Isomorphism Rigidity for Generic Finitely Presented Groups

Let $F_m=F(a_1,\dots,a_m)$ with $m\ge 2$, and fix $q\ge 1$. For every fixed $0<\lambda<1$, we prove that a $q$-tuple $\mathbf W_n$ of independent uniformly random cyclically reduced words of length $n$ is \emph{$\lambda$-stable} with probability converging to $1$ exponentially fast. Namely, for every $\Phi\in Aut(F_m)$...

Ilya Kapovich · 0 citations