Multiple choice

For the composition table of a cyclic group shown below

* a b c d
a a b c d
b b a d c
c c b d a
d d c a b

Which one of the following choices is correct?

  1. a, b are generators

  2. b, c are generators

  3. c, d are generators

  4. d, a are generators
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

a * a = a. So a can not generate anything other than a. In fact a is identity so a can not be generator.

So this eliminates Option A & D.

b*b = a. Also a is just identity, so b*a=a*b = a. So b can not generate all elements . So Option B is out.

So Answer is C.

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