College Algebra Exam Review 253

College Algebra Exam Review 253 - 5.6. ADDITIONAL EXERCISES...

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Unformatted text preview: 5.6. ADDITIONAL EXERCISES FOR CHAPTER 5 263 5.6.17. Let G be a finite group, p a prime, and P a p –Sylow subgroup. Suppose H is a normal subgroup of G of order p k for some k . Show that H Â P. 5.6.18. Show that a group of order 2n 5m , m; n subgroup. Can you generalize this statement? 1, has a normal 5–Sylow 5.6.19. Show that a group G of order 56 has a normal Sylow subgroup. Hint: Let P be a 7–Sylow subgroup. If P is not normal, count the elements [ in gP g 1 . g 2G ...
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.

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