大门|大门-CS-2009 |问题60

对于如下所示的循环群的组成表

以下哪个选项是正确的？ （A） a、 b是发电机 （B） b、 c是发电机 （C） c、 d.发电机 （D） d、 a是发电机 答复: （C） 说明：

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

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