Invariable generation of finite classical groups

Eilidh McKemmie

Published 2019-10-08Version 1

A subset of a group invariably generates the group if it generates even when we replace the elements by any of their conjugates. The probability that four randomly selected elements invariably generate $S_n$ is bounded below by an absolute constant for all $n$, but for three elements, the probability tends to zero as $n \rightarrow \infty$ [Eberhard-Ford-Green, Pemantle-Peres-Rivin]. We prove an analogous result for the finite classical groups using the fact that most elements of classical groups are separable and the correspondence between classes of maximal tori containing separable elements in classical groups and conjugacy classes in their Weyl groups.