25.22 RightCoset for Ag Groups

AgGroupOps.Coset( G )

A coset C = <G>{*}x is represented as record with the following components.

representative:

contains the representative x.

group:

contains the group G.

isDomain:

is true.

isRightCoset:

is true.

isFinite:

is true.

operations:

contains the operations record RightCosetAgGroupOps.

RightCosetAgGroupOps.<( C1, C2 )

If C1 and C2 do not have a common group or if one argument is no coset then the functions uses DomainOps.< in order to compare C1 and C2. Note that this will compute the set of elements of C1 and C2.

If C1 and C2 have a common group then AgGroupCosetOps.< will use SiftedAgWord (see SiftedAgWord) and ConjugateSubgroup (see ConjugateSubgroup) in order to compare C1 and C2. It does not compute the set of elements of C1 and C2.

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GAP 3.4.4
April 1997