If we are (as is usual) concerned at a particular time with only the left or the right coset space, then the superscript is usually dropped and the notation $G / H$ is used for both the left and right coset space.
If, in addition, $H$ is a normal subgroup of $G$, then $G / H^l = G / H^r$ and the notation $G / H$ is then unambiguous anyway.
Also known as
Some sources call this the left quotient set and right quotient set respectively.
Some sources use:
- $G \mathrel \backslash H$ for $G / H^l$
- $G / H$ for $G / H^r$
This notation is rarely encountered, and can be a source of confusion.