Re: [代數] 代數(2)
※ 引述《PttFund (批踢踢基金只進不出)》之銘言：
: Show that a group of order 30 cannot be a simple group.
可以推廣到order為 2qr的群 where 2<q<r are primes.
The key point is that, by sylow theorem,
the number of k-sylow is greater than k since the group is not simple.
With this, we can estime the size of the group:
2qr >= 1+3*1+(q+1)(q-1)+(r-1)(r+1)
= 2+q^2+r^2
which is impossible.
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