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Homework Help
Calculus and Beyond Homework Help
Showing two groups are *Not* isomorphic
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[QUOTE="DeldotB, post: 5246386, member: 562269"] [h2]Homework Statement [/h2] Good day, I need to show: [tex]\mathbb{Z}_{4}\oplus \mathbb{Z}_{4} [/tex]is not isomorphic to [tex]\mathbb{Z}_{4}\oplus \mathbb{Z}_{2}\oplus \mathbb{Z}_{2}[/tex] [h2]Homework Equations[/h2] None [h2]The Attempt at a Solution[/h2] I was given the hint that to look at the elements of order 4 in a group. I know [tex]\mathbb{Z}_{4}\oplus \mathbb{Z}_{4} [/tex] will have the elements: (0,0)(0,1)(0,2)(0,3)(1,0)(1,1)...(3,3). Im a little confused on how to find the order of say (1,2) in [tex]\mathbb{Z}_{4}\oplus \mathbb{Z}_{4} [/tex]. I know how to find the order of say <3> in [tex]\mathbb{Z}_{4}[/tex] (order=4/gcd(3,4)=4) but how can I do it with the direct sum elements? Thanks in advance! [/QUOTE]
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Calculus and Beyond Homework Help
Showing two groups are *Not* isomorphic
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