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Class ProductGroup

Object
  AbstractCollection
      AbstractSet
          ImmutableSet
              Group
                  HashGroup
                      ProductGroup

All Implemented Interfaces:

Collection, Set

Direct Known Subclasses:

ProductGroupInternal

public class ProductGroup

extends HashGroup

A direct product G₁ × G₂ of two Groups.

Author:

Mark McConnell

Field Summary

Fields inherited from class Group

charTable

Constructor Summary

ProductGroup(Group factor1, Group factor2)

Method Summary

protected void	fillInCharTable() Takes the characters currently in the character tables of the factors, pull them back to the product, takes all the tensor products of the pullbacks, and puts them in the character table of the product.
protected Comparator	getCharComparator() The characters of a ProductGroup always appear in lexicograhic order based on the order of the characters for the factors.
Group	getFactor1()
Group	getFactor2()
Homomorphism	getProductMorphism(Homomorphism f1, Homomorphism f2) Fills in the dotted arrow in the diagram that defines "direct product" in the category of groups.
Homomorphism	getProjection1() The canonical projection map from G1 × G2 to G1.
Homomorphism	getProjection2() The canonical projection map from G1 × G2 to G2.
static Group	iteratedProduct(List list) Returns the iterated product of the Groups G1 through Gk making up the given List.
static void	main(String[] args) Tests the product of C_n's whose orders are specified by the arguments.
String	toString()

Methods inherited from class HashGroup

contains, getConjClass, getConjClassIndex, getConjClassNum, iterator, size

Methods inherited from class Group

cyclicSubgpsUpToConj, describeOrder8, elementarySubgps, getCenter, getCentralizer, 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

Methods inherited from class Object

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

Methods inherited from interface Set

containsAll, isEmpty, toArray, toArray

Constructor Detail

ProductGroup

public ProductGroup(Group factor1,
                    Group factor2)

Method Detail

iteratedProduct

public static Group iteratedProduct(List list)

Returns the iterated product of the Groups G₁ through G_k making up the given List. It is a ProductGroup of the following form:

G₁ × (G₂ × (G₃ × ... × G_k)).

If there is only one group G₁, it is returned directly. If the List is empty, null is returned.

getFactor1

public final Group getFactor1()

getFactor2

public final Group getFactor2()

getProjection1

public Homomorphism getProjection1()

The canonical projection map from G₁ × G₂ to G₁.

getProjection2

public Homomorphism getProjection2()

The canonical projection map from G₁ × G₂ to G₂.

getProductMorphism

public Homomorphism getProductMorphism(Homomorphism f1,
                                       Homomorphism f2)

Fills in the dotted arrow in the diagram that defines "direct product" in the category of groups.

Parameters:

f1 - A homomorphism from some group A to G₁.

f2 - A homomorphism from A to G₂.

Returns:

The product morphism from A to G₁ × G₂.

Throws:

IllegalArgumentException - If the A's are not the same, or the G's are not those of this product group.

fillInCharTable

protected void fillInCharTable()
                        throws OrthonormalityException

Takes the characters currently in the character tables of the factors, pull them back to the product, takes all the tensor products of the pullbacks, and puts them in the character table of the product.

Overrides:

fillInCharTable in class Group

Throws:

OrthonormalityException - If the table isn't full at the end, or if anything goes wrong in the middle.

getCharComparator

protected Comparator getCharComparator()

The characters of a ProductGroup always appear in lexicograhic order based on the order of the characters for the factors.

Overrides:

getCharComparator in class Group

toString

public String toString()

main

public static void main(String[] args)

Tests the product of C_n's whose orders are specified by the arguments.