I know I need to use Sylow's theorems, I would normally find how many Sylow p subgroups there are of each prime factor and then work out whether they are unique or not to determine if they're simple. But since 2017 is prime, I don't know how to go about it, any ideas?
Is a group of order 2017 simple?
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$\begingroup$
abstract-algebra
group-theory
finite-groups
sylow-theory
simple-groups
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0The only odd simple groups are the ones of prime order. – 2017-02-10
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1Any group of prime order is both simple and cyclic. – 2017-02-10
1 Answers
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It is simple, because if $H$ is a subgroup of $G$ with $|G|=2017$, then $|H|$ would divide 2017 by Lagrange's theorem. So $|H|=1$ or $|H|=2017$