作者Sfly (entangle)
看板Math
标题Re: [代数] 代数(2)
时间Sun Jul 24 16:03:49 2005
※ 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.
--
※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 220.135.132.108
1F：推 PttFund:神 <(_ _)>140.112.218.142 07/24
2F：推 LimSinE:可推广到pqr, p,q,r相异质数。 61.70.211.116 07/24
3F：推 Sfly:yeah220.135.132.108 07/24