Factor Group or Quotient Group of $G$ by $N$, or $G/N$

Please Login to access more options.

Definition (Factor Group or Quotient Group of $G$ by $N$, or $G/N$)

Let $G$ be a group. Let $N$ be a normal subgroup of $G$. Then we define the factor group of $G$ by $N$, or the quotient group of $G$ by $N$, to be the set $G/N = \{Na\mid a\in G\}$, i.e the collection of right cosets of $N$ using the set product $(Na)(Nb)=N(ab)$ as the binary operation.

The following pages link to this page.