Group-theoretic commutator and group action

Description

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

Usage

1
commutator(x, y)

Arguments

x,y

Permutation objects, coerced to word

Author(s)

Robin K. S. Hankin

See Also

group_action

Examples

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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