作者elvolvo (沉醉东风...)
看板Math
标题Re: [代数] 代数(5)
时间Sun Jul 24 16:57:40 2005
※ 引述《PttFund (批踢踢基金只进不出)》之铭言：
: Let G be an abelian group of order 360.
: (a) How many Sylow 3-subgroups does G have?
Because G is abelian, every subgroup of G is normal in G.
Hence G has only one Sylow 3-subgroup.
: (b) Up to isomorphism, describe all the possible structures of G.
By fundamental theorem of finite abelian groups, we have
G = Z_360 ps: Z_m x Z_n = Z_mn if and only if (m,n)=1
= Z_180 x Z_2
.
.
.
(依此类推)
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 140.122.140.213
※ 编辑: elvolvo 来自: 140.122.140.213 (07/24 16:59)
1F：推 PttFund:就把 360 质因数分解 @O@140.112.218.142 07/24