作者Zebulon (你对我的好)
看板Math
标题Re: [代数] 代数(2)
时间Sun Jul 24 19:26:20 2005
※ 引述《Sfly (entangle)》之铭言：
: ※ 引述《PttFund (批踢踢基金只进不出)》之铭言：
: : Show that a group of order 30 cannot be a simple group.
: 可以推广到order为 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.
还有一个有趣的事
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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