Re: [代數] 代數(2)
※ 引述《Sfly (entangle)》之銘言：
: ※ 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.
還有一個有趣的事
If G is a group of order 2k, where k is odd,
then G has a subgroup H of order k.
Therefore H is a proper normal subgroup of G. G is not simple.
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