repthy
Class D_2n

Object
  AbstractCollection
      AbstractSet
          ImmutableSet
              Group
                  HashGroup
                      PermGp
                          D_2n

All Implemented Interfaces:

Collection, Set

public class D_2n

extends PermGp

The dihedral group D_2n of order 2n, for n geq 3. It is realized in degree n with standard generators R = (0 1 2 ... n-1) and E = (0 n-1)(1 n-2)... .

Author:

Mark McConnell

Field Summary

Fields inherited from class Group

charTable

Constructor Summary

D_2n(int n)
Constructor.

Method Summary

protected void	fillInCharTable() Handles the dihedral case directly.
Subgroup	getCyclicSubgroup() Returns the cyclic subgroup generated by R, as a Subgroup.
PermGpElt	getE() Returns the generator E.
PermGpElt	getR() Returns the generator R.
PermGpElt	getRpwr(int i) Returns the i-th power of the generator R.
PermGpElt	getRpwrE(int i) Returns R^i E.
boolean	isSimple() Always false, since n geq 3.
static void	main(String[] args) For testing the dihedral group of order 2n.

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, getSylow, 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

D_2n

public D_2n(int n)

Constructor.

Throws:

IllegalArgumentException - Unless n is greater than or equal to 3.

Method Detail

fillInCharTable

protected void fillInCharTable()
                        throws OrthonormalityException

Handles the dihedral case 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.

getRpwr

public PermGpElt getRpwr(int i)

Returns the i-th power of the generator R. We don't require i to lie between 0 and n.

getRpwrE

public PermGpElt getRpwrE(int i)

Returns R^i E. We don't require i to lie between 0 and n.

getR

public PermGpElt getR()

Returns the generator R.

getE

public PermGpElt getE()

Returns the generator E.

getCyclicSubgroup

public Subgroup getCyclicSubgroup()

Returns the cyclic subgroup generated by R, as a Subgroup.

isSimple

public final boolean isSimple()

Always false, since n geq 3.

Overrides:

isSimple in class Group

main

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

For testing the dihedral group of order 2n. Takes one argument n.

Throws:

OrthonormalityException