The maximal number of elements pairwise generating the symmetric group of even degree

Francesco Fumagalli, Martino Garonzi, Attila Maróti

Published 2020-11-29Version 1

Let $G$ be the symmetric group of even degree at least $26$. We compute the maximal size of a subset $S$ of $G$ such that $\langle x,y \rangle = G$ whenever $x,y \in S$ and $x \neq y$, and we show that it is equal to the covering number of $G$, that is, to the minimal number of proper subgroups of $G$ whose union is $G$.