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How to show that the group ( Z 4 , + 4 ) is isomorphic to ( i , *) ?

How to show that the group ( Z4 , + 4 ) is isomorphic to ( i , *)?

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2 Answers

Arif Hossain
askIITians Faculty 52 Points
8 years ago
first you have to show that there exist an homomorphisim from( Z4, + 4 ) to( i , *) after that if this homomorphisim is a monomorphisim as well as an epimorphisim i.e.,homomorphisim is ono-one and onto then its isomorphic
mycroft holmes
272 Points
8 years ago
Take the mapping n -----> in. where n is an integer. Its easy to check that its a homomorphism with kernel 4Z. Hence, by the first isomorphism theorem the coset Z/4Z i.e. Z4 is isomorphic to the image i.e {i,-1,i,1}

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