What does the notation $G /^r H$ mean?

Question

$G /^r H$

I saw this notation in an answer to a question and am not sure what it means.

The exact context is as follows:

$G=Sym(5)$ acts on the set $G/^r H$ of all right cosets of $H$ in $G$.

It would help if you could include the context. It might mean the right cosets of $H$ in $G$. — Eric Auld, Nov 21 '13 at 04:35

score 2 · Accepted Answer · answered Nov 21 '13 at 05:15

Space of right cosets. When $H$ is normal, you'd just interpret $G/H$ as the quotient space. But when it's just a subgroup, $G/H$ represents a coset space. But there are two distinct ones, so you need a way to distinguish them. That answer used a superscript $r$ to denote right cosets. I've also seen $H\backslash G$ for right cosets (and then $G/H$ means left cosets).

What does the notation $G /^r H$ mean?

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