MAT-3110 Midterm: MATH 3110 App State Fall2009 Test3 answer key

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15 Feb 2019
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4 x2, y, xy, x2y, x3y x, x3 order = element = November 20th, 2009: (16 points) the following groups are not isomorphic. Notice that both of these groups are of order 10, but that"s about the only property that matches. On the other hand, z10 has elements of order 1, 2, 5, and 10. Both d4 and q are non-abelian groups of order 8. Let"s try looking at the order of each element. This shows us that these groups cannot be isomorphic. For example, d4 has 5 elements of order 2 while. Q only has 1 element of order 2: (14 points) is it possible? (a) let g1 and g2 be groups of order 7. If so, give examples of non-isomorphic groups of order 7. We know that groups of prime order are cyclic and any two cyclic groups of the same order are isomorphic.

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