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Test Corrections

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strom
5 diapositives · 176 Views · Jul 23, 2014

Submit corrected answers for a chance to regain lost points—follow honor code. Complete separate sheets by Tuesday. Review isomorphism questions with justifications. Additional exercises provided.

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Test Corrections
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  1. Test Corrections • You may correct the in-class portion of your test. You will get back 1/2 of the points you lost if you submit correct answers. • This work is to be done on your own (or in consultation with me only). Skidmore Honor Code! • Corrections should be done on separate sheets, NOT on the original test. Hand both things in, NOT stapled together. • Due on Tuesday (10/22) at 4:45.

  2. Some Exercises on Isomorphisms Etc. (10/18/13) • On yes-no questions, A is yes and B is no. G and G’ are non-trivial abstract groups. • “OP” means operation-preserving. • Whatever your response, think of justification: • Is every OP function from G to G’ an isomorphism? • Is every 1-to-1 and onto function from G to G’ an isomorphism? • Is every automorphism an isomorphism? • Is every isomorphism an automorphism? • Is every automorphism of G a permutation of G? • Is every permutation of G an automorphism of G?

  3. Exercises Continued • Whatever your response, think of justification: • Is R90 in D4 isomorphic to U(8)? • Is Z4 isomorphic to U(10)? • Is U(125) isomorphic to U(184)? • Is R (under +) isomorphic to R+ (under times)? • Is Q(under +) isomorphic to Q+(under times)? • Is 7Z isomorphic to 8Z? • Does S6 contain subgroups isomorphic to S4? • (If so, how many do you think?) • Does A6contain subgroups isomorphic to D4?

  4. Exercises Continued • Whatever your response, think of justification: • In Z10, if  takes 1 to 6, is  an automorphism? • In Z10, if  takes 1 to 9, is  an automorphism? • In Z,if  takes 1 to 6, is  an automorphism? • In Z, if  takes 1 to 6, is  an isomorphism? • In C, is the “conjugate mapping”  which takes x + iy to x – i y an automorphism? • In D4, if takes R90 to R180, is  an automorphism? • In D4, if  takes R90 to R270, D to D’, and H to V, do you think  is an automorphism?

  5. Assignment for Monday • Work on Test Corrections! • We will set Monday aside for an optional question and answer period. At that time we can discuss issues arising in the test corrections and also issues from the take-home part. Please look at the answer key on that part before coming to that class. • Keep working on Chapter 6.