hw23 - a Prove that H f = σ ∈ S n | σf = f is a...

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Modern Algebra 1 Homework 11.2 Spring 2010 Due April 14 Exercise 4. Determine if the permutations in Exercise 1 are even or odd. Exercise 5. Prove that a cycle in S n is even if and only if its length is odd. Exercise 6. Let f ( x 1 ,x 2 ,...,x n ) be a function of n variables ( n 2).
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Unformatted text preview: a. Prove that H f = { σ ∈ S n | σf = f } is a subgroup of S n . b. If f ( x 1 ,x 2 ,x 3 ,x 4 ) = x 1 + x 2 + x 3 x 4 show that H f ∼ = Z 2 × Z 2 c. Find a polynomial f ( x 1 ,x 2 ,x 3 ,x 4 ) so that H f = h (1234) , (13) i ....
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This note was uploaded on 02/29/2012 for the course MATH 3362 taught by Professor Ryandaileda during the Spring '10 term at Trinity University.

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