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Let $|G| = pq^n$ for $p primes and $n$ is in the natural numbers

a) Show there is $H$ a normal subgroup of $G$ with $|H|=q^n$

b) If $P$ is a normal subgroup of $G$ with $|P| = p$, show that for any $m$ with $m$ divides $|G|$, there is $H_m$ (a subgroup of $G$) with $|H_m| =m$.

I am completely lost on how to start this, so any help would be appreciated, thanks!

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    Are p,q prime ?2012-12-18
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    yes p, q are prime with p2012-12-18
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    Also, is p2012-12-18
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    yes p2012-12-18

2 Answers 2