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# First Isomorphism Theorem Question watch

1. Can f:Z/4Z----> <i> (cyclic group generated by complex number i) where f(n)= i^n be group isomorphism. A question that i got asked assumes it is. However here I have this problem: Z/4Z={4Z,4Z+1,4Z+2.4Z+3} so f(4Z+1)=i for 0 and positive integers and f(4Z+1)= -1/i for negative integers... so f is not bijective. Shouldn't Z/4Z quotient group be replaced by N/4N quotient group for f to be group isomorphism.
2. I don't see how you've deduced the two different expressions, but in any event, -1/i = i, so they are the same thing.

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Updated: November 7, 2017
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