I've only recently started looking at quotient groups, so I don't know if this question will make sense...
In this wiki article, $G/H$ is defined as the set of left cosets of $H$ in $G$, without any reference to whether or not $H$ is normal. In the quotient group article, however, the definition of is stated only for when $H$ is a normal subgroup of $G$.
- What accounts for the discrepancy between the two articles?
- Are quotient groups only defined when $H \triangleleft G$?
- If one is trying to determine what $G/H$ is explicitly, will this be affected if $H$ is normal or not? Are there any caveats I should anticipate if $H$ is not normal?
I do want to note that I came across a similar article, but I don't understand it all.