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Unformatted text preview: MATH 373: Final Exam Monday, May 3, 2010 • Answer all questions in the answer booklet. Please do these in order. • You are expected to justify your answers in a manner that an average MATH 373 student should be able to follow. This includes sentences for clarification. • Questions are on both sides of the page. This test is worth a total of 200 points. 1. Quickies  Provide a short justification (one sentence). [50 pts] (a) In Q [ x ] / x 2 x + 3 is it true that x 2 x 3 + x 2 x + 3 = 6 + x 2 x + 3 ? (b) T or F: x 10 + 12 x 9 3 x 7 + 21 x 5 6 x 3 + 300 x 2 15 x + 12 is irreducible over Q . (c) The set of odd integers under addition is not a group. What is missing? (d) Suppose H ≤ S 5 with  H  = 10. How many cosets of H are in S 5 ? (e) T or F: If σ ∈ S n then o ( σ )  n . (recall: o ( σ ) = order of σ ) (f) T or F: If G is a group with 15 elements then G is isomorphic to a subgroup of S 15 ....
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This note was uploaded on 04/19/2011 for the course MATH 21373 taught by Professor Johnson during the Spring '11 term at Carnegie Mellon.
 Spring '11
 Johnson
 Math, Algebra

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