Uses of Class
repthy.Group

Uses of Group in repthy

Subclasses of Group in repthy

class	A_n The group A_n consisting of all even permutations of n elements.
class	AbelianGroup What's purple and commutes?
class	C_n The cyclic group C_n of order n with generator g.
class	D_2n The dihedral group D_2n of order 2n, for n geq 3.
class	GL The general linear group GL(n, p) over the finite field of p elements.
class	HashGroup An implementation of Group backed by a HashSet that holds one copy of each element of the group.
class	PermGp A HashGroup in which all the group elements are PermGpElts of the same degree.
class	PGL The general linear group PGL(n, p) over the finite field of p elements.
class	PGroup A p-group, that is, a group of order pm where p is a prime and m ≥ 0.
class	ProductGroup A direct product G1 × G2 of two Groups.
class	ProductGroupInternal An internal direct product, where the elements g1, g2 in g1 × g2 lie in a common parent group.
class	PSL The projective special linear group PSL(n, p) over the finite field of p elements.
class	PSL3 Special topics concerning PSL3(p) for a prime p.
class	PSL3b Special topics concerning PSL3(p) for a prime p.
class	Q_8 The quaternionic group of order 8.
class	QuotientGroup 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 QuotientGroup.getQuotientMap() for obtaining the quotient homomorphism from G to G/H.
class	S_n The group Sn consisting of all permutations of the integers 0, ..., n-1.
class	SL The special linear group SLn(p) over the finite field of p elements.

Methods in repthy that return Group

Group	ProductGroupInternal.asInternal()
static Group	PSL3b.getW(int p)
Group	AbelianGroup.getSNF() Returns a group with the same elements as this, but exhibited in Smith normal form with the ProductGroup structure as shown.
static Group	ProductGroup.iteratedProduct(List list) Returns the iterated product of the Groups G1 through Gk making up the given List.
Group	ProductGroup.getFactor1()
Group	ProductGroup.getFactor2()
Group	Homomorphism.getSource() Returns the source (domain).
Group	Homomorphism.getTarget() Returns the target.
Group	ClassFunction.getGroup() Returns the underlying group.
Group	Subgroup.getGroup() Returns the ambient group G.
Group	Subgroup.getSubgroup() Returns the subgroup H itself.
Group	Subgroup.sg() An alias for Subgroup.getSubgroup().
Group	CharTable.getGroup() Returns the underlying group.

Methods in repthy with parameters of type Group

int	QuotientGroupElt.getOrder(Group G)
int	ProductGroupElt.getOrder(Group G)
int	MatrixModp.getOrder(Group G)
int	PermGpElt.getOrder(Group G) This implementation ignores G.
static HashHomom	HashHomom.make(Group sou, GroupElt[] souGen, Group tar, GroupElt[] tarImages) Returns the homomorphism from sou to tar sending the generators souGen to the corresponding elements tarImages, or returns null to indicate that such a homomorphism does not exist.
static Homomorphism	Homomorphism.identity(Group G, Group G1) If G and G1 have the same elements (that is, if G.equals(G1)), this method returns the natural identity map from G to G1.
int	GroupElt.getOrder(Group G) Returns the order of this element.
static int	Group.getEltOrder(GroupElt g, Group G) Finds the order of the element g.
boolean	Group.isSubgroupOf(Group G1) Whether this is a subgroup of G1.
static void	Group.printTest(Group G) Prints all (yes, all) the elements and conjugacy classes to standard output.
static void	Group.tableTest(Group G, String nameG) For testing; displays the character table in a window and decomposes some sample representations.

Constructors in repthy with parameters of type Group

ProductGroupInternal(Group factor1, Group factor2)
Constructor.

AbelianGroup(Group G)
Given a Group, this constructs an AbelianGroup with the same elements.

HomomFromFunc(Group sou, Group tar, HomomorphismFunc f)

ProductGroup(Group factor1, Group factor2)

HashHomom(Group sou, Group tar, Map map)
Constructs a homomorphism from sou to tar.

ClassFunction(Group G, Complex[] val)
Constructs the class function on G whose value on the i-th conjugacy class (as returned by getConjClass(int)) is val[i].

GpCharacter(Group G, Complex[] val, int cycloField)
Constructs the character on G whose value on the i-th conjugacy class (as returned by getConjClass(int)) is val[i].

GpCharacter(Group G, Complex[] val, int cycloField, String name)
Same as the three-argument constructor, but allows the user to specify the name.

GpCharacter(Group G, int type)
Constructs the specified character on G.

Subgroup(Group G, Group H)

Subgroup(Group G, int type)
Constructor for special cases.

CharTable(Group G)
Constructs an empty character table for G.

PGroup(Group s, int p)
Given a Group and a prime p, this constructs a p-group with the same elements.