s09_mthsc851_midterm2

s09_mthsc851_midterm2 - MTHSC 851 Midterm 2 Spring 2009...

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Unformatted text preview: MTHSC 851, Midterm 2 Spring 2009 Instructor: Dr. Matthew Macauley Thursday, April 9, 2009 Name Instructions • Exam time is 75 minutes • You may not use notes or books. • PLEASE WRITE NEATLY AND COMPLETELY! Work out what you want to say on scratch paper before you write it out on the test. There are two pages of scratch paper at the end. • If you have any doubt about what results you may assume, then ask . Question Points Earned Maximum Points 1 15 2 15 3 25 4 25 5 20 Total 100 Student to your left: Student to your right: 1. Carefully and fully state each of the following definitions. [Be sure to give definitions, not notation or equivalent descriptions.] (a) Define the ascending central series of a group G , and use that to say what it means for G to be a nilpotent group. (b) Let H be a subgroup of a group G . Define the normalizer of H in G . 2. Carefully state (but do not prove) each of the indicated results. Be sure to put in all the hypotheses, and the complete conclusions.complete conclusions....
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s09_mthsc851_midterm2 - MTHSC 851 Midterm 2 Spring 2009...

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