Timothy C. Burness

On the regularity of irreducible subgroups of finite classical groups

Let $G$ be a finite group and let $\tau = (H_1, \ldots, H_t)$ be a $t$-tuple of core-free subgroups of $G$. We say that $\tau$ is regular if $G$ contains elements $g_1, \ldots, g_t$ such that $\bigcap_i H_i^{g_i} = 1$, which is equivalent to the existence of a regular $G$-orbit on the Cartesian product $G/H_1 \times \c...