Prove that \{0} \{0}) is not isomorphic to \{0} (the group operation in both cases is multiplication).
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Originally Posted by Jimmy_W Prove that \{0} \{0}) is not isomorphic to \{0} (the group operation in both cases is multiplication). suppose there was an isomorphism let and then thus hence at least one of is equal to why? but then and so hence at least one of is equal to which is obviously impossible!
You can just say these groups cannot be isomorphic due to the fact that has elements of order 4, namely while there are no elements of order 4 in everything in has order one: (1,1) two: (-1,1), (1,-1) and (-1,-1) or infinite order: everything else
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