Term for a permutation group every element of which except of identity has no fixed points

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A permutation group on a set $D$ is a group whose elements are functions on $D$ and whose composition is function composition.

Is there a term for a permutation group every element of which except of identity has no fixed points?

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It is called a semi-regular permutation group.

From Encyclopedia of Mathematics

Permutation group

A permutation group is called semi-regular (or freely acting) if the stabilizer of each point is the identity group and regular (or simply transitive) if the group is also transitive