Arithmetic with Elements

Contents

u * v : GrpBBElt, GrpBBElt -> GrpBBElt
Construct the product of elements u and v of the BB-group G.
u ^ m : GrpBBElt, RngIntElt -> GrpBBElt
Given an integer m and u, an element of BB-group G, return the element of G corresponding to the m-th power of u.
u ^ v : GrpBBElt, GrpBBElt -> GrpBBElt
Given u and v, elements of BB-group G, return the element of G corresponding to the conjugate of u by v, i.e. v - 1 * u * v.
(u, v) : GrpBBElt, GrpBBElt -> GrpBBElt
Commutator of the elements u and v, i.e. the element u - 1 * v - 1 * u * v. Here u and v must belong to the same BB-group G.

Accessing the Defining Generators

The functions described here provide access to basic information stored for a BB-group G.

G . i : GrpBB, RngIntElt -> GrpBBElt
The i-th generator for G.
Generators(G) : GrpBB -> { GrpBBElt }
A set containing the generators for G.
NumberOfGenerators(G) : GrpBB -> RngIntElt
Ngens(G) : GrpBB -> RngIntElt
The number of generators for B.
V2.28, 13 July 2023