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Class QuotientGroup

Object
  AbstractCollection
      AbstractSet
          ImmutableSet
              Group
                  HashGroup
                      QuotientGroup

All Implemented Interfaces:

Collection, Set

public class QuotientGroup

extends HashGroup

Given a Subgroup (G, H) where H is a normal subgroup of G, this class is the quotient group G/H, and provides the method getQuotientMap() for obtaining the quotient homomorphism from G to G/H.

Author:

Mark McConnell

Field Summary

Fields inherited from class Group

charTable

Constructor Summary

QuotientGroup(Subgroup GcontainingH)
Constructor.

Method Summary

Homomorphism	getQuotientMap()
Subgroup	getSubgp() Returns the Subgroup (G, H) that was used to construct this group G/H.
static void	main(String[] args) As a test, prints a description of S4/(Klein 4-group), which should be S3.

Methods inherited from class HashGroup

contains, getConjClass, getConjClassIndex, getConjClassNum, iterator, size

Methods inherited from class Group

cyclicSubgpsUpToConj, describeOrder8, elementarySubgps, fillInCharTable, getCenter, getCentralizer, getCharComparator, getCharTable, getCommutatorSubgroup, getCompositionSeries, getConjClassRep, getEltOrder, getEltOrder, getIdentity, getOrder, getProperNormalSubgroup, getSylow, isAbelian, isCentral, isSimple, isSubgroupOf, order, power, printTest, tableTest

Methods inherited from class ImmutableSet

add, addAll, clear, remove, removeAll, retainAll

Methods inherited from class AbstractSet

equals, hashCode

Methods inherited from class AbstractCollection

containsAll, isEmpty, toArray, toArray, toString

Methods inherited from class Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Methods inherited from interface Set

containsAll, isEmpty, toArray, toArray

Constructor Detail

QuotientGroup

public QuotientGroup(Subgroup GcontainingH)

Constructor.

Throws:

IllegalArgumentException - If H is not normal in G.

Method Detail

getSubgp

public Subgroup getSubgp()

Returns the Subgroup (G, H) that was used to construct this group G/H.

getQuotientMap

public Homomorphism getQuotientMap()

main

public static void main(String[] args)

As a test, prints a description of S₄/(Klein 4-group), which should be S₃.