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Unformatted text preview: a A and a A . Are the left cosets the same as the right cosets? 3. Suppose that f : G H is a homomorphism, and K is a subgroup of H. We dene the inverse image of K under f to be f1 ( K ) = { x G : f ( x ) K } . Show that f1 ( K ) is a subgroup of G. Note: We are not assuming that f is a bijection, and therefore f1 does not mean inverse function here. Instead, f1 ( K ) is shorthand for a particular subset of G. 4. Problem 2.4 #16. Hint: Consider the elements in G that are their own inverses, and the ones that are not. 5. Problem 2.5 #12. 6. Problem 2.5 #16. 7. Problem 2.5 #20. Hint: Think about the element mnm1 n1 . 1...
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This note was uploaded on 08/25/2011 for the course MATH 4107 taught by Professor Staff during the Spring '10 term at University of Florida.
 Spring '10
 Staff
 Math, Algebra

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