arXiv subjects
Publications and source records attributed to Colva Roney-Dougal.
We show that given generators for subgroups $G$ and $H$ of $\mathrm{S}_n$, if $G$ is primitive then generators for $\mathrm{N}_H(G)$ may be computed in quasipolynomial time, namely $2^{O(\log^3 n)}$. The previous best known bound was simply exponential.
Helfgott proved that there exists a $δ>0$ such that if $S$ is a symmetric generating subset of $SL(2,p)$ containing 1 then either $S^3=SL(2,p)$ or $|S^3|\geq |S|^{1+δ}$. It is known that $δ\geq 1/3024$. Here we show that $δ\leq(\log_2(7)-1)/6 \approx 0.3012$ and we present evidence suggesting that this might be the true value of $δ$.