# 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 $B$.