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  • Sho w that G 1 G 2 and G 2 G 1 are isomorphic.Exercise If o ( a 1 ) = m and o ( a 2 ) = n; nd the order of ( a 1 ; a 2 ) in G 1 G 2 Exercise Sho w that if G is an y group of order 4, G is isomorphic to Z 4 or Z 2 Z 2 Sho w Z 4 is not isomorphic to Z 2 Z 2 : Sho w Z 12 is isomorphic to Z 4 Z 3 : Finally sho w that Z mn is isomorphic to Z m Z n i ( m; n ) = 1.
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