repthy
Class Q_8

Object
  AbstractCollection
      AbstractSet
          ImmutableSet
              Group
                  HashGroup
                      PermGp
                          Q_8

All Implemented Interfaces:

Collection, Set

public class Q_8

extends PermGp

The quaternionic group of order 8.

List the elements in the order
1, i, -1, -i, j, k, -j, -k.
Then left multiplication by i is
(0 1 2 3)(4 5 6 7),
and left multiplication by j is
(0 4 2 6)(1 7 3 5).

Author:

Mark McConnell

Field Summary

Fields inherited from class Group

charTable

Constructor Summary

Q_8()
Constructor.

Method Summary

protected void	fillInCharTable() This group is handled directly.
Subgroup	getSylow(int p) Returns one of the Sylow p-subgroups of this group, as a Subgroup in which the underlying subgroup is a PGroup.
boolean	isSimple() Whether this group is simple.
static void	main(String[] args) For testing.

Methods inherited from class PermGp

getDegree

Methods inherited from class HashGroup

contains, getConjClass, getConjClassIndex, getConjClassNum, iterator, size

Methods inherited from class Group

cyclicSubgpsUpToConj, describeOrder8, elementarySubgps, getCenter, getCentralizer, getCharComparator, getCharTable, getCommutatorSubgroup, getCompositionSeries, getConjClassRep, getEltOrder, getEltOrder, getIdentity, getOrder, getProperNormalSubgroup, isAbelian, isCentral, 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

Q_8

public Q_8()

Constructor.

Method Detail

fillInCharTable

protected void fillInCharTable()
                        throws OrthonormalityException

This group is handled directly.

Overrides:

fillInCharTable in class Group

Throws:

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

isSimple

public final boolean isSimple()

Description copied from class: Group

Whether this group is simple.

Overrides:

isSimple in class Group

getSylow

public Subgroup getSylow(int p)

Description copied from class: Group

Returns one of the Sylow p-subgroups of this group, as a Subgroup in which the underlying subgroup is a PGroup.

Overrides:

getSylow in class Group

main

public static void main(String[] args)
                 throws OrthonormalityException

For testing.

Throws:

OrthonormalityException