Let $g$, $h$ be a random pair of generators of $G=Sym(n)$ or $G=Alt(n)$. We show that, with probability tending to $1$ as $n\to \infty$, (a) the diameter of $G$ with respect to $S =… Expand

Let G be a permutation group on a finite set Ω. A subset of Ω is a base for G if its pointwise stabilizer in G is trivial. The base size of G, denoted b(G), is the smallest size of a base. A… Expand

We study `good elements' in finite $2n$-dimensional classical groups $G$: namely $t$ is a `good element' if $o(t)$ is divisible by a primitive prime divisor of $q^n-1$ for the relevant field order… Expand

In this note we present a simplified and slightly generalized version of a lemma the authors published in 1987. The lemma as stated here asserts that if the order of a permutation of $n$ elements is… Expand