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 \(G\).