Math787_HW2 - P )) = N G ( P ). 3. Let G be a finite group...

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Math 787: Preparation for Algebra Qualifying Exam, Summer 2008. Homework II: Group Theory 1. Let G be a non-abelian group of order p 3 for some prime p . Show that Z ( G ) = G 0 . 2. Let G be a finite group and P a Sylow subgroup. Show that N G ( N G (
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Unformatted text preview: P )) = N G ( P ). 3. Let G be a finite group of order 105. Show that it has an element of order 15. 4. Show that a group of order 5 × 7 × 17 is cyclic. 5. If | G | = 108, show G is solvable. 1...
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This note was uploaded on 07/17/2008 for the course MATH 787 taught by Professor Joshua during the Summer '08 term at Ohio State.

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