 Subgroup correspondence for a surjective group homomorphism (source code)

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= Subgroup correspondence for a surjective group homomorphism
{title2=$B\longleftrightarrow\theta^{-1}(B),\qquad A\longleftrightarrow\theta(A)\quad(K\leq A)$}

For a <surjection> $\theta:G\to H$ with kernel $K$, inverse image and image give inverse order-preserving <bijections> between <subgroups> of $H$ and <subgroups> of $G$ containing $K$. They preserve index. For an arbitrary <subgroup> $A$, $\theta^{-1}(\theta(A))=AK$, so $[H:\theta(A)]=[G:AK]$.

// Target: algebra.bigb

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