In Aschbacher's paper about automorphism groups of symmetric block designs, there is mention of "standard $(G,\pi)$ pairs" and "standard permutation groups":
If $G$ is a permutation group on a set $\Omega$ and $\pi$ is a set of primes, the pair $(G, \pi)$ is said to be standard if, for all $p \in \pi$ and $g \in G$ with $|g| = p$, we have that $G^{F(g)}$ is a $\pi^{\prime}$-group, where, $G^{F(g)}$ is the group induced by $G$ acting faithfully on the fixed points of $g$, and being a $\pi^{\prime}$ group means that the only primes dividing $|G^{F(g)}|$ are in $\pi^{\prime}$ (complement of $\pi$).
This mostly seems to be used as a tool to show that a group action in "standard":
$G$ is defined to be a standard permutation group if every non-trivial element of $G$ has the same set of fixed points. We remark that if $G$ is standard then every non-trivial orbit of $G$ has length $|G|$.
This is equivalent to $G$ acting semiregularly on $\Omega$ after the fixed points are removed; but it is a good tool for investigating the possible actions of a given group on a set (such as determining the possible automorphism groups of a combinatorial design with certain parameters, along with their cycle structure).
This terminology does not seem to be very common (or rather it is incredibly too common - a search for "permutation group standard pair" leads to many many hits with various meanings); is there a more standard (ha)/modern term for these properties of a group action? And/or a reference that can explain more about this?
Aschbacher, Michael, On collineation groups of symmetric block designs, J. Comb. Theory, Ser. A 11, 272-281 (1971). ZBL0223.05006.