Answer to Question #203299 in Abstract Algebra for Dag stern

Question

The table below is a Cayley table for the group ({e,a,b,c,d},∗). Fill in the blanks.

e a b c d

_______________________

e e e - - -

a - b - - e

b - c d e -

c - d - a b

d - - - - -

_______________________

Answer 1

Solution:

It is given that ({e,a,b,c,d},∗) is a group.

So, we have

$a*b=b*a=c \\b*c=c*b=d \\c*d=d*c=a \\ a*d=d*a=b \\b*d=d*b=c \\a*c=c*a=b \\a*a=b*b=c*c=d*d=e$

Then, we have following table: