Documentation

group-action
- Action of PSL₂(R) on the Upper Half Plane (CONGRUENCE SUBGROUPS OF PSL₂(R))
- Automorphism Groups (LINEAR CODES OVER FINITE FIELDS)
- Group Actions on Polynomials (INVARIANT THEORY)
group-actions
- Group Actions (LINEAR CODES OVER FINITE FIELDS)
group-algebra
- Group Algebras (ALGEBRAS WITH INVOLUTION)
group-Boolean
- General Group Properties (ABELIAN GROUPS)
group-boolean
- General Group Properties (POLYCYCLIC GROUPS)
group-braid
- Braid Groups (COXETER GROUPS)
group-code-design
- Construction from Groups, Codes and Designs (GRAPHS)
group-cohomology
- Finite Group Cohomology (COHOMOLOGY AND EXTENSIONS)
group-elt-op
- Operations on Elements (COXETER GROUPS)
group-op
- Operations on Coxeter Groups (COXETER GROUPS)
group-order
- Group Order (MATRIX GROUPS OVER GENERAL RINGS)
- Group Order (PERMUTATION GROUPS)
group-overview
- GROUPS
group-prop
- Properties of Coxeter Groups (COXETER GROUPS)
group-properties
- Basic Group Properties (FINITE SOLUBLE GROUPS)
group-props
- GrpPC_group-props (Example H69E4)
group-recognition
- Group Recognition (ALMOST SIMPLE GROUPS)
group-simple
- ALMOST SIMPLE GROUPS
group-theory
- Group Theoretic Functions (CLASS FIELD THEORY)
group-wgraphs
- W-graphs (COXETER GROUPS)
Group4
- Group4P(o, i) : RngIntElt, RngIntElt -> Grp
- IdentifyGroup4P(G) : GrpPC -> RngIntElt
Group4P
- Group4P(o, i) : RngIntElt, RngIntElt -> Grp
group_points
- The Order of the Group of Points (ELLIPTIC CURVES OVER FINITE FIELDS)
GroupActions
- RngInvar_GroupActions (Example H117E1)
GroupAlgebra
- GroupAlgebra(S) : AlgGrpSub -> AlgGrp
- GroupAlgebra( R, G: parameters ) : Rng, Grp -> AlgGrp
- GroupAlgebra(R, G) : Rng, Grp -> AlgGrp
- AlgBas_GroupAlgebra (Example H92E1)
GroupAlgebraAsStarAlgebra
- GroupAlgebraAsStarAlgebra(R, G) : Rng, Grp -> AlgGrp
- AlgInv_GroupAlgebraAsStarAlgebra (Example H94E3)
GroupAlgebraAsStarAlgebra2
- AlgInv_GroupAlgebraAsStarAlgebra2 (Example H94E4)
GroupComputation
- GrpAb_GroupComputation (Example H75E6)
GroupConstructors
- Grp_GroupConstructors (Example H63E4)
GroupData
- GroupData(D, i): DB, RngIntElt -> Rec
GroupIdeal
- GroupIdeal(F) : FldInvar -> RngMPol
- GroupIdeal(R) : RngInvar -> RngMPol
GroupName
- GroupName(G) : Grp -> MonStgElt
groupname
- Names of Finite Groups (GROUPS)
GroupOfLieType
- GroupOfLieType(L) : AlgLie -> GrpLie
- GroupOfLieType(C, k) : AlgMatElt, Rng -> GrpLie
- GroupOfLieType(W, k) : GrpMat, Rng -> GrpLie
- GroupOfLieType(W, k) : GrpPermCox, Rng -> GrpLie
- GroupOfLieType(W, R) : GrpPermCox, Rng -> GrpLie
- GroupOfLieType(W, q) : GrpPermCox, RngIntElt -> GrpLie
- GroupOfLieType(N, k) : MonStgElt, Rng -> GrpLie
- GroupOfLieType(N, q) : MonStgElt, RngIntElt -> GrpLie
- GroupOfLieType(C, k) : Mtrx, Rng -> GrpLie
- GroupOfLieType(C, q) : Mtrx, RngIntElt -> GrpLie
- GroupOfLieType(R, k) : RootDtm, Rng -> GrpLie
- GroupOfLieType(R, k) : RootDtm, Rng -> GrpLie
- GroupOfLieType(R, q) : RootDtm, RngIntElt -> GrpLie
GroupOfLieTypeFactoredOrder
- GroupOfLieTypeFactoredOrder(R, q) : RootDtm, RngElt -> RngIntElt
GroupOfLieTypeHomomorphism
- GroupOfLieTypeHomomorphism(phi, k) : Map, Rng -> .
- GroupOfLieTypeHomomorphism(phi, k) : Map, Rng -> GrpLie
GroupOfLieTypeOrder
- GroupOfLieTypeOrder(R, q) : RootDtm, RngElt -> RngIntElt
- RootDtm_GroupOfLieTypeOrder (Example H104E11)
GroupOrders
- Cartan_GroupOrders (Example H102E15)
Groups
- NumberOfGroups(D) : DB -> RngIntElt
- # D : DB -> RngIntElt
- # D : DB -> RngIntElt
- # D : DB -> RngIntElt
- # D : DB -> RngIntElt
- # D : DB -> RngIntElt
- AdmissableTriangleGroups() : -> SeqEnum
- GeneratepGroups (p, d, c : parameters) : RngIntElt, RngIntElt,RngIntElt -> [GrpPC], RngIntElt
- IsolGroupsOfDegreeFieldSatisfying(d, p, f) : RngIntElt, RngIntElt, Any -> SeqEnum
- IsolGroupsOfDegreeSatisfying(d, f) : RngIntElt, Any -> SeqEnum
- IsolGroupsSatisfying(f) : Any -> SeqEnum
- NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
- NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
- NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
- NumberOfGroups(D, d) : DB, RngIntElt -> RngIntElt
- NumberOfGroups(D, o) : DB, RngIntElt -> RngIntElt
- NumberOfGroups(D, o1, o2): DB, RngIntElt, RngIntElt -> RngIntElt, RngIntElt
- NumberOfIrreducibleMatrixGroups(k, p) : RngIntElt, RngIntElt -> RngIntElt
- NumberOfPrimitiveGroups(d) : RngIntElt -> RngIntElt
- NumberOfSimpleGroups() : -> RngIntElt
- NumberOfSmallGroups(o) : RngIntElt -> RngIntElt
- NumberOfTransitiveGroups(d) : RngIntElt -> RngIntElt
- PicardToClassGroupsMap(X) : TorVar -> Map
- PrimitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
- PrimitiveGroups(d, f: parameters) : RngIntElt, Program -> [GrpPerm]
- PrimitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
- QuasisimpleMatrixGroups(): -> SeqEnum
- SmallGroups(o: parameters) : RngIntElt -> [* Grp *]
- SmallGroups(o, f: parameters) : RngIntElt, Program -> [* Grp *]
- SmallGroups(S: parameters) : [RngIntElt] -> [* Grp *]
- SmallGroups(S, f: parameters) : [RngIntElt], Program -> [* Grp *]
- ThreeIsogenySelmerGroups(E : parameters) : CrvEll -> GrpAb, Map, GrpAb, Map, MapSch
- TransitiveGroups(d: parameters) : RngIntElt -> [GrpPerm]
- TransitiveGroups(S: parameters) : [RngIntElt] -> [GrpPerm]
- TransitiveGroups(d, f) : RngIntElt, Program -> [GrpPerm]
- TransitiveGroups(S, f) : [RngIntElt], Program -> [GrpPerm]
- TwoIsogenySelmerGroups(E) : CrvEll[FldFunG] -> GrpAb, GrpAb, MapSch, MapSch
- WeilToClassGroupsMap(C) : RngCox -> Map

V2.28, 13 July 2023

Magma is maintained and distributed by the Computational Algebra Group, School of Mathematics and Statistics, University of Sydney.