对于如下所示的循环群的组成表
|
* |
a |
b |
c |
d |
|
a |
a |
b |
c |
d |
|
b |
b |
a |
d |
c |
|
c |
c |
d |
b |
a |
|
d |
d |
c |
a |
b
|
以下哪个选项是正确的?
(A) a, b 是生成器
(B) b, c 是发电机
(C) c, d 是发电机
(D) d, a 是生成器答案： (C)
解释：
Check for all:-
a1 = a ,
a2 = a * a = a
a3 = a2 * a = a * a = a
a is not the generator since we are not able to express
other members of the group in powers of a
Check for c -
c1 = c
c2 = c * c = b
c3 = c2 * c = b * c = d
c4 = c2 * c2 = b * b = a
We are able to generate all the members of the group from c ,
Hence c is the generator
Similarly check for d
这个问题的测验