permutation group

permutation group (plural permutation groups)

1. (algebra, group theory) A group whose elements are permutations (self-bijections) of a given set and whose group operation is function composition.
   • 1979, Norman L. Biggs, A. T. White, Permutation Groups and Combinatorial Structures, page 80,

     In this chapter we shall be concerned with the relationship between permutation groups and graphs. We begin by explaining how a transitive permutation group may be represented graphically, and then we reverse the process, showing that a graph gives rise to a permutation group.

   • 1996, Helmut Volklein, Groups as Galois Groups: An Introduction, page 47,

     The Galois group G(L_f /C(x)) is called the monodromy group of f, denoted Mon(f), and viewed as a permutation group on the conjugates of y over C(x).

   • 2002, Peter J. Cameron, B.5 Permutation Groups, Alexander V. Mikhalev, Günter F. Pilz (editors), The Concise Handbook of Algebra, page 86,

     Now, groups are axiomatically defined, and the above concept is a permutation group, that is, a subgroup of the symmetric group. […] The study of finite permutation groups is one of the oldest parts of group theory, motivated initially by its connection with solvability of equations.

• (group whose elements are permutations of a set): transformation group

• (group whose elements are permutations of a set): alternating group, symmetric group

• permutation representation