7.96 Double Coset Records

A double coset is represented by a domain record with the following tag components.

isDomain:

always true.

isDoubleCoset:

always true.

The double coset is determined by the following identity components, which every double coset must have.

leftGroup:

the left subgroup U.

rightGroup:

the right subgroup V.

representative:

an element of the double coset. It is unspecified which element.

In addition, a double coset record may have the following optional information components.

rightCosets:

a list of disjoint right cosets of the left subgroup U, whose union is the double coset.

elements:

if present the proper set of elements of the double coset.

isFinite:

if present this is true if the double coset is finite and false if the double coset is infinite. If not present it is not known whether the double coset is finite or infinite.

size:

if present the size of the double coset. Is "infinity" if the coset is infinite. If not present the size of the double coset is not known.

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