Let $G$ be a finite group acting regularly and transitively on a set $X$, so that $|G| = |X|$. Can the action of $G$ also be primitive?
2026-04-05 17:10:54.1775409054
Regular primitive permutation groups
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Yes, it's primitive if and only if $|G|$ is prime.
In general a transitive group $G$ is primitive if the stabilizer of a point is a maximal subgroup of $G$. In this case the point stabilizer if the trivial subgroup, which is maximal if and only if $|G|$ is prime.