math 435 sample exam 1

# math 435 sample exam 1 - Sample Questions for Midterm 1...

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Sample Questions for Midterm 1, MATH 435 Problem 1 [ Review the definitions and theorems covered so far. You will be asked to state a few of them precisely. ] Problem 2 [ Review the TRUE / FALSE questions of the relevant sections. ] Problem 3 Let G be a group. An automorphism is an isomorphism f : G G . Let Aut( G ) be the set of all automorphisms of G . Show that Aut( G ) with the binary operation of composition is a subgroup of S G , the symmetric group of G . Problem 4 Let A be the square below. 1 2 3 4 90 0 σ τ Let σ be the symmetry of the square given by counter-clockwise rotation by 90
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