QuotientGroupMap

QuotientGroupMap

Represents a Quotient Group G/N, providing a mapping between elements of the quotient group (as permutations on coset indices) and their representatives in the original group G.

Constructor

new QuotientGroupMap(quotientGroup, representatives, quotientOrder)

Source:
Parameters:
Name Type Description
quotientGroup PermutationSet

A PermutationSet whose elements act on the coset indices (0-based).
representatives Int32Array

An Int32Array where representatives[i] is a chosen representative from the i-th coset.
quotientOrder bigint

The order of the quotient group, |G/N|.

Methods

lift(quotientPermId) → {number}

Description:

  • Lifts a quotient group element (represented by a permutation ID) back to a specific representative element in the original group G. The returned element g is such that the quotient element corresponds to the coset Ng.

Source:
Parameters:
Name Type Description
quotientPermId number

The ID of the permutation in the quotient group.
Throws:

If the quotientPermId maps to an invalid coset index.

Type
Error
Returns:

The ID of a representative element in the original group G.

Type
number