MAT-3110 Midterm: MATH 3110 App State Fall2011 Test2
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/20 points) cyclic (a) let g = hgi where g has order 20. hg8i = Why or why not? (b) suppose g is a cyclic group with at least one element of order 6. Is there more than one possibility? (c) list the possible orders of elements in z33. Then determine the number of elements of each order. /20 points) the following pairs of groups are not isomorphic. Prove this is the case. (a) gl3(r) 6 = a500 (b) u (8) = {1, 3, 5, 7} 6 = z4 (c) gl2(z) 6 = q (d) s4 6 = d12. /20 points) isomorphisms (a) prove that u (5) = z4. (b) let g be an abelian group. De ne the map : g g by (g) = g 1. Prove that is an isomorphism (actually is an automorphism since its domain and codomain are equal). Does anyone actually read the directions to these problems? (a) let = (2453)(1346)(126) s6.
