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For questions related to teaching mathematics. For questions in Mathematics Education as a scientific discipline there is also the tag mathematics-education. Note you may also ask your question on http://matheducators.stackexchange.com/.

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What is the standard 2-generating set of the symmetric group good for?

Let $f\in\mathbb{Q}[x]$ be an irreducible polynomial of prime degree $p$, with exactly $2$ non-real roots. You can view the Galois group of $f$ (i.e., the Galois group of the splitting $f$) as a subgr …
Thomas Browning's user avatar