Moderate# Presentation of a Group: Generators and Relations (Relators)

ABSALG-LXTKN3

Let $F=F(B)$ be a free group with basis $B$ and let $R$ be a set of reduced words on $B$.

A group $G$ is said to be the group defined by generators $b\in B$ and relations (or relators) $r\in R$, when:

$G=F/N$ where $N=N(R)$ is the normal subgroup of $F$ "generated by $R$".

The subgroup $N$ is the intersection of all normal subgroups of $F$ that contain $R$.

We write $G=\langle B\mid r=1, r\in R\rangle$.

Notation: $A_n$ denotes the alternating group (the subgroup of even permutations in $S_n$), $n\ge 2$.

Which of the following are **TRUE**?

Select **ALL** that apply.