permutations: commutator – R documentation

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commutator

Group-theoretic commutator and group action

Description

Group-theoretic commutator, defined as [x,y]=x^(-1)y^(-1)xy

Usage

commutator(x, y)

Arguments

x,y

Permutation objects, coerced to word

Author(s)

Robin K. S. Hankin

Examples

x <- rperm(10,7)
y <- rperm(10,8)
z <- rperm(10,9)

uu <- 
commutator(commutator(x,y),z^x) *
commutator(commutator(z,x),y^z) *
commutator(commutator(y,z),x^y) 

stopifnot(all(is.id(uu)))  # this is the  Hall-Witt identity

permutations

The Symmetric Group: Permutations of a Finite Set

v1.0-9

GPL-2

Authors

Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>), Paul Egeler [ctb] (<https://orcid.org/0000-0001-6948-9498>)

Initial release