Question
Let $H$ and $K$ be subgroups of a finite group $G$ with $H \subseteq K \subseteq G$. Prove that $|G: H|=|G: K||K: H|$.
Step 1
The index notation $|G:H|$ denotes the number of distinct left cosets of $H$ in $G$. In other words, it is the number of distinct sets of the form $gH = \{gh : h \in H\}$, where $g \in G$. Show more…
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