Arithmetic with Elements

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.