FREE GROUPS
Acknowledgements
Introduction
Free Groups and Words
Construction of a Free Group
Construction of Words
Access Functions for Words
Arithmetic Operators for Words
Comparison of Words
String Operations on Words
Finitely Generated Subgroups of Free Groups
The Automorphism Group of a Free Group
Bibliography
Introduction
Free Groups and Words
Construction of a Free Group
FreeGroup(n) : RngIntElt -> GrpFP
Example GrpFree_Free (H78E1)
Construction of Words
G ! [ i1, ..., is ] : GrpFP, [ RngIntElt ] -> GrpFPElt
Identity(G) : GrpFP -> GrpFPElt
Random(G, m, n) : GrpFP, RngIntElt, RngIntElt -> GrpFPElt
Access Functions for Words
# w : GrpFPElt -> RngIntElt
ElementToSequence(w) : GrpFPElt -> [ RngIntElt ]
ExponentSum(w, x) : GrpFPElt, GrpFPElt -> RngIntElt
GeneratorNumber(w) : GrpFPElt -> RngIntElt
LeadingGenerator(w) : GrpFPElt -> GrpFPElt
Parent(w) : GrpFPElt -> GrpFP
Example GrpFree_WordAccess (H78E2)
Arithmetic Operators for Words
u * v : GrpFPElt, GrpFPElt -> GrpFPElt
u ^ n : GrpFPElt, RngIntElt -> GrpFPElt
u ^ v : GrpFPElt, GrpFPElt -> GrpFPElt
(u, v) : GrpFPElt, GrpFPElt -> GrpFPElt
(u1, ..., un) : List(GrpFPElt) -> GrpFPElt
Comparison of Words
u eq v : GrpFPElt, GrpFPElt -> BoolElt
u ne v : GrpFPElt, GrpFPElt -> BoolElt
u lt v : GrpFPElt, GrpFPElt -> BoolElt
u le v : GrpFPElt, GrpFPElt -> BoolElt
u ge v : GrpFPElt, GrpFPElt -> BoolElt
u gt v : GrpFPElt, GrpFPElt -> BoolElt
Example GrpFree_Words (H78E3)
String Operations on Words
Eliminate(u, x, v) : GrpFPElt, GrpFPElt, GrpFPElt -> GrpFPElt
Eliminate(U, x, v) : { GrpFPElt }, GrpFPElt, GrpFPElt -> { GrpFPElt }
Match(u, v, f) : GrpFPElt, GrpFPElt, RngIntElt -> BoolElt, RngIntElt
RotateWord(u, n) : GrpFPElt, RngIntElt -> GrpFPElt
Substitute(u, f, n, v) : GrpFPElt, RngIntElt, RngIntElt, GrpFPElt -> GrpFPElt
Subword(u, f, n) : GrpFPElt, RngIntElt, RngIntElt -> GrpFPElt
Example GrpFree_WordOps (H78E4)
Finitely Generated Subgroups of Free Groups
Supergroup(F) : GrpFP -> GrpFP
x in H: GrpFP, GrpFPElt -> BoolElt
IsSubgroup(H, K) : GrpFP, GrpFP -> BoolElt
H eq K : GrpFP, GrpFP -> BoolElt
Index(F, H) : GrpFP, GrpFP -> RngIntElt
HasFiniteIndex(F, H) : GrpFP, GrpFP -> BoolElt
FreeGenerators(H) : GrpFP -> SeqEnum, GrpFP
H meet K : GrpFP, GrpFP -> GrpFP
Centraliser(F,x) : GrpFP, GrpFPElt -> GrpFP
IsConjugate(F, x, y) : GrpFP, GrpFPElt, GrpFPElt -> BoolElt, GrpFPElt
Centraliser(F, H) : GrpFP, GrpFP -> GrpFP
Normaliser(F, H) : GrpFP, GrpFP -> GrpFP
IsConjugate(F, H, K) : GrpFP, GrpFP, GrpFP -> BoolElt, GrpFPElt
Example GrpFree_free-subgroups (H78E5)
The Automorphism Group of a Free Group
AutomorphismGroup(F) : GrpFP -> GrpAuto
InverseAutomorphismFreeGroup(F, Q) : GrpFP, SeqEnum -> GrpAutoElt
WhiteheadReduction(F, Q) : GrpFP, SeqEnum -> BoolElt, SeqEnum, GrpAutoElt
Example GrpFree_FreeAut (H78E6)
Example GrpFree_FreeAut2 (H78E7)
Bibliography
[Next][Prev] [Right] [____] [Up] [Index] [Root]
|