Definition:Coset Space/Notation

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Coset Space: Notation

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.

Thus 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.

Some sources use $G \divides H$ 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.