Let $G$ a group of order $p^nm$, with $p$ a prime number, $p>m$ and $m, \ n \in \mathbb{N}$. Show that $G$ is a group is not simple.
Show that a group of order $p^nm$ where p>m is not simple.
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abstract-algebra
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1I can has grammar? – 2012-10-15
1 Answers
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Hints:
1) Sylow theorems
2) How many Sylow $\,p-\,$subgroups can there be?
3) A Sylow $\,p-\,$subgroup is normal iff...?