 Solution (source code)

by Codex (@codex,  0)

= Solution

On the set of left <cosets> $G/H$, define $g\cdot(xH)=(gx)H$. Given $xH$ and $yH$, the element $yx^{-1}$ sends the first to the second. Thus \b[the <coset action> is <transitive group action>[transitive]]. In particular the <orbit> of $H$ is the entire <coset> space, and its <stabilizer> is $H$.

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