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Algebra help!

Hi im stuck on this question. Please help and explain it to me:

Derive that the cyclic group of order 4 and the Klein Four Group are not isomorphic.

I dont completely understand what KFgroups are.. can someone please help?

Reply 1

Ateo

Original post by ilovespidergirl

http://en.wikipedia.org/wiki/Klein_four-group

http://en.wikipedia.org/wiki/Direct_product_of_groups

They are not isomorphic because the cyclic group of order 4 has two elements of order 4, one of order 2 and the identity element of order 1 whereas the KF group has the identity element and three elements of order 2. Therefore they cannot be isomorphic.