# hw6 - 4 Let G be a ﬁnite group and let p be the smallest...

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Math 4124 Monday, March 14 Sixth Homework Due 2:30 p.m., Monday March 21 1. Section 4.2, Exercise 2 on page 121. (3 points) 2. Let N ± S 5 , and suppose N 6 = 1 or S 5 . (a) Determine the conjugacy classes of S 5 and their size. (b) Show that N cannot contain a transposition. (c) Prove that N = A 5 . (4 points) 3. Section 4.3, Exercise 5 on page 130. (2 points)
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Unformatted text preview: 4. Let G be a ﬁnite group and let p be the smallest prime dividing | G | (assume that G 6 = 1). If H ± G and | H | = p , prove that H ≤ Z ( G ) (consider | K ( x ) | for 1 6 = x ∈ H ; it should be clear that | K ( x ) | ≤ p-1 ) . (3 points) (4 problems, 12 points altogether)...
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## This note was uploaded on 01/02/2012 for the course MATH 4124 taught by Professor Staff during the Spring '08 term at Virginia Tech.

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