Question

We use bracket notation and not bar notation

In Episode 57, we determined that the Cayley table of a group G of order 4 in which some element is not its own inverse is as follows: e *le a b c a b c e b bb с a cbae a a с e с Show that every element of G is a power of a; in particular, G = {e, a, a?, a} and a' = e. Write the Cayley table for G using this notation.

Answer 1

e a b c b с C e С a e b a e С C axa =C since clearly from Table so a²=c similarly c*a = b axa xa b a3 = b and we have axb -e a * a a = e so clearly G= { e, a, b, c b=a², c=a², a4=e Now has 2 e 3 e e a a3 a a2 a2 a3 a3 e a2 a2 e a a3 93 е a² Ans