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 \(B\).