- Introduction
- Construction of a Finitely Presented Abelian Group and its Elements
- Construction of a Generic Abelian Group
- Elements
- Construction of Subgroups and Quotient Groups
- Standard Constructions and Conversions
- AbelianGroup(GrpAb, Q) : Cat, [ RngIntElt ] -> GrpAb
- AbelianGroup(G) : Grp -> GrpAb, Hom
- AbelianQuotient(G) : Grp -> GrpAb, Hom
- DirectSum(A, B) : GrpAb, GrpAb -> GrpAb
- PCGroup(A) : GrpAb -> GrpPC, Hom(Grp)
- PermutationGroup(A) : GrpAb -> GrpPerm, Hom(Grp)
- FPGroup(A) : GrpAb -> GrpFP, Hom(Grp)
- CommutatorSubgroup(G) : GrpAb -> GrpAb
- CommutatorSubgroup(H, K) : GrpAb, GrpAb -> GrpAb
- Centralizer(G, a) : GrpAb, GrpAbElt -> GrpAb
- Core(G, H) : GrpAb, GrpAb -> GrpAb
- Centre(G) : GrpAb -> GrpAb
- FittingGroup(G) : GrpAb -> GrpAb
- Hypercentre(G) : GrpAb -> GrpAb
- Operations on Elements
- Order of an Element
- Order(x) : GrpAbElt -> RngIntElt
- Example GrpAb_DiscreteLog (H75E10)
- Order(g: parameters) : GrpAbGenElt -> RngIntElt
- Order(g, l, u: parameters) : GrpAbGenElt, RngIntElt, RngIntElt -> RngIntElt
- Order(g, l, u, n, m: parameters) : GrpAbGenElt, RngIntElt, RngIntElt ,RngIntElt, RngIntElt -> RngIntElt
- Discrete Logarithm
- Equality and Comparison
- Invariants of an Abelian Group
- Canonical Decomposition
- Set-Theoretic Operations
- Coset Spaces
- Subgroup Constructions
- Subgroup Chains
- General Group Properties
- IsCyclic(G) : GrpAb -> BoolElt
- IsElementaryAbelian(G) : GrpAb -> BoolElt
- IsFree(G) : GrpAb -> BoolElt
- IsMixed(G) : GrpAb -> BoolElt
- IspGroup(G) : GrpAb -> BoolElt
- DerivedLength(G) : GrpAb -> RngIntElt
- Properties of Subgroups
- IsMaximal(G, H) : GrpAb, GrpAb -> BoolElt
- Index(G, H) : GrpAb, GrpAb -> RngIntElt
- FactoredIndex(G, H) : GrpAb, GrpAb -> [<RngIntElt, RngIntElt>]
- IsPure(G, H) : GrpAb, GrpAb -> BoolElt
- IsNeat(G, H) : GrpAb, GrpAb -> BoolElt
- Enumeration of Subgroups
- Representation Theory
- The Hom Functor
- Automorphism Groups
- Cohomology
- Homomorphisms
- hom< A -> B | L> : Grp, Grp, List -> Map
- Homomorphism(A, B, X, Y) : Grp, Grp, [ GrpElt ], [ GrpElt ] -> Map
- iso< A -> B | L> : Grp, Grp, List -> Map
- Isomorphism(A, B, X, Y) : Grp, Grp, [ GrpElt ], [ GrpElt ] -> Map
- Example GrpAb_Homomorphisms (H75E15)
- Bibliography
V2.28, 13 July 2023