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Sylow Theorem Examined

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Let G be a group so that |G|=p^2q^n, for p, q primes with q > p >=3. Show that G is not simple. Hint: Look at the q-Sylow subgroups. There cannot be p of them so what happens if there are P2 of them?

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We consider the Sylow q-subgroup of G with |G| = p^2 * q^n.
By the Sylow theorem, assume the number of Sylow q-subgroup is k, then we ...

Solution Summary

Sylow Theorem is contextualized.