GroupGenerators

The generating permutations a PermutationGroup was built from, in Cycles notation — or, for AlternatingGroup, the fixed pair Wolfram itself uses.

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GroupGenerators(group)the generators passed to PermutationGroup, unchanged; or AlternatingGroup(n)'s canonical pair

Typed signatures

Type	Package	Applies
`(expression<AlternatingGroup> \| expression<PermutationGroup>) -> list<expression<Cycles>>`	`groupalgebra`	always

Domain: Permutations

Examples

Basic #

\mathrm{GroupGenerators}(\mathrm{PermutationGroup}(\bigl\lbrack\mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 9, 6\bigr\rbrack, \bigl\lbrack3, 7\bigr\rbrack\bigr\rbrack)\bigr\rbrack))

Out

\bigl\lbrack\mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 9, 6\bigr\rbrack, \bigl\lbrack3, 7\bigr\rbrack\bigr\rbrack)\bigr\rbrack

A group built from generators returns them as given

\mathrm{GroupGenerators}(\mathrm{PermutationGroup}(\bigl\lbrack\mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack\bigr\rbrack), \mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 3\bigr\rbrack, \bigl\lbrack2, 4\bigr\rbrack\bigr\rbrack)\bigr\rbrack))

Out

\bigl\lbrack\mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack\bigr\rbrack), \mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 3\bigr\rbrack, \bigl\lbrack2, 4\bigr\rbrack\bigr\rbrack)\bigr\rbrack

Scope #

Generators of the Klein four-group, kept in order

\mathrm{GroupGenerators}(\mathrm{PermutationGroup}(\bigl\lbrack\mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack), \mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 3\bigr\rbrack, \bigl\lbrack2, 4\bigr\rbrack\bigr\rbrack)\bigr\rbrack))

Out

\bigl\lbrack\mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack), \mathrm{Cycles}(\bigl\lbrack\bigl\lbrack1, 3\bigr\rbrack, \bigl\lbrack2, 4\bigr\rbrack\bigr\rbrack)\bigr\rbrack

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