On the regularity number of a finite group and other base-related
invariants
On the regularity number of a finite group and other base-related
invariants
A $k$-tuple $(H_1, \ldots, H_k)$ of core-free subgroups of a finite group $G$ is said to be regular if $G$ has a regular orbit on the Cartesian product $G/H_1 \times \cdots \times G/H_k$. The regularity number of $G$, denoted $R(G)$, is the smallest positive integer $k$ with the property that …