[代數] 請幫我看看我做的對不對(有2題)
先說聲對不起喔,過了個暑假,對代數一整個變生疏了
所以想請各位大大幫忙看一下=D"
Let <(3,3)> be the cyclic subgroup of Z9xZ6 generated by (3,3) and let L
be the quotient group Z9xZ6/<(3,3)>.
1. Find the order |L|.
sol: |L|=|Z9xZ6/<(3,3)>|=|Z9xZ6|/|<(3,3)>|
因為 <(3,3)>={(3,3),(6,0),(0,3),(3,0),(6,3),(0,0)}
所以 |L|=9x6/6=9
---
True or false. With a reason.
Let G be the group of order 40. If g 屬於 G such that g^20 =\= e (where e is
the identity of G), then G is cyclic and generated by g.
sol: False.
反例:
Let G=Z5xZ8 and g=(0,1). Then g^8=(0,0), g^20=\=(0,0). Clearly, G=\=<(0,1)>.
---
不好意思,只是簡單的兩題,卻沒什麼把握= ="
請鞭小力一點,如果有錯或是有更好的想法請告訴我,謝謝 >口<"
(晚點可能會在放一題上來= =...)
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.40.220.113
→
09/04 12:51, , 1F
09/04 12:51, 1F
→
09/04 16:17, , 2F
09/04 16:17, 2F
→
09/04 19:29, , 3F
09/04 19:29, 3F
推
09/04 21:39, , 4F
09/04 21:39, 4F