Definition:Coset Space/Right Coset Space

Definition
Let $G$ be a group, and let $H$ be a subgroup of $G$. The right coset space (or family) of $G$ modulo $H$ is denoted $G / H^r$ and is the set of all the right cosets of $H$ in $G$.

Note
If we are (as is usual) concerned at a particular time with only the right or the left coset space, then the superscript is usually dropped and the notation $G / H$ is used for both the right and left 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.

Alternative Terminology
Some sources call this the right quotient set.

Some sources use $G \backslash H$ for the left coset space, reserving $G / H$ for the right coset space.

This notation is rarely encountered, and can be a source of confusion.