# permutation group

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

**permutation group** (*plural* **permutation groups**)

- (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**.

- In this chapter we shall be concerned with the relationship between
**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*).

- The Galois group G(
**2002**, Peter J. Cameron,*B.5*, Alexander V. Mikhalev, Günter F. Pilz (editors),**Permutation Groups***The Concise Handbook of Algebra*, page 86,- Now, groups are axiomatically defined, and the above concept is a
, that is, a subgroup of the symmetric group. […] The study of finite**permutation group****permutation groups**is one of the oldest parts of group theory, motivated initially by its connection with solvability of equations.

- Now, groups are axiomatically defined, and the above concept is a

#### Synonyms[edit]

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

#### Hyponyms[edit]

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

#### Related terms[edit]

#### Translations[edit]

group whose elements are permutations