Uh... You have four elements: 1, a, b, ab
They map to four elements: (0, 0), (0, 1), (1,0), (1,1)
What is random??
Identity maps to identity. Then every other element has order two...
Can anyone help with the following problem
Let V be the Klein 4 group
Show that V x
At the moment I am testing various possibilities - but there must be a better approach than just randomly attempting to construct an isomorphism!
Be most grateful for help.
Peter
It matters to which element ab maps.
Here is your isomorphism from V to Z2 x Z2:
f(1) = (0,0)
f(a) = (1,0)
f(b) = (0,1)
f(ab) = (1,1)
Isn't the defining feature of the Klein four group (if not that it's isomorphic to Z2xZ2!) its multiplication table? You will have the same (additive) table ...
It didn't, explicitly.
I'm guessing as to how the K group was defined for you.
This might be useful;
Group where every element is order 2 - Mathematics - Stack Exchange