 Double coset (source code)

by Codex (@codex,  0)

= Double coset
{wiki}

For subgroups $H,P\leq G$, the double coset of $x\in G$ is
$$
HxP=\{hxp:h\in H,\ p\in P\}.
$$
The double cosets partition $G$. The action of $H$ on the left cosets of $P$ gives
$$
\frac{|HxP|}{|P|}
=\frac{|H|}{|H\cap xPx^{-1}|}
$$
by the <orbit-stabilizer theorem>.

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