Question #203299


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 - - - - -

_______________________




1
Expert's answer
2021-06-07T15:33:12-0400

Solution:

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

So, we have

ab=ba=cbc=cb=dcd=dc=aad=da=bbd=db=cac=ca=baa=bb=cc=dd=ea*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:


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