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College Algebra Exam Review 253

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

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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 P . 5.6.18. Show that a group of order 2 n 5 m , m; n 1 , has a normal 5 –Sylow subgroup. Can you generalize this statement?
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