A subgroup of the symmetric group of a set, acting faithfully by permutations. A finite permutation group specified by generators can be enumerated by repeatedly multiplying the elements already found by those generators until no new element appears. Its orbits and conjugacy classes can then be computed directly.
The historical study of permutations of letters or quantities and their compositions, closely connected with the development of group theory and the theory of polynomial equations.
A permutation group on a set is oligomorphic when its diagonal action on ordered -tuples has finitely many orbits for every positive integer . For a countable model of a complete theory, an oligomorphic automorphism group makes every finite-arity type space finite: realized types are dense, and only finitely many are possible because types are constant on orbits.
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A permutation group is a mathematical concept in group theory that consists of a set of permutations of a given set combined with the operation of composition. Here's a more detailed breakdown of the concept: 1. **Permutations**: A permutation of a set is a rearrangement of its elements. For a finite set with \( n \) elements, a permutation is simply a bijective function from the set to itself.
