Complete the group as isomorphic

[Anarchy6k2]

1. Complete the following table to obtain a Group, G, that is isomorphic to Z4
2. Complete the same table to obtain a Group, H, that is NOT isomorphic to Z4

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


I tried to complete the group as isomorphic, can anyone tell me if this is correct?

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

And here is my attempt at part to as if it is not an isomorphism


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

 

[Hurkyl]

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

You're saying that this is the multiplication table for a group? What's the inverse of b?

 

[CrazyCalcGirl]

:(

All I can say is LOL you might want to work on the table with all a's in it. It has to follow group properties. I hope that's not the grade you want in this class.

 

[CrazyCalcGirl]

ok here

ok now that you got rid of all those crazy a's here is what I got.

Part 1. isomorphic to Z4
abcd
bcda
cdab
dabc

part 2. not isomorphic to Z4
abcd
badc
cdab
dcba

Anyone else get this?

 

[Anarchy6k2]

Thanks, I was talking it over with some friends and we all got the same thing. Thanks for the assistance haha now I can definatly get an A ^_^

 

[HallsofIvy]

Yes, all groups of order 4 are either isomorphic to Z₄ or the Klein 4 group.

CrazyCalcGirl- please do NOT give complete answers in the homework section.