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22.7. If m and n are positive integers and m|n,then is a normal subgroup of (inZ). What is |/|? Justify your answer.

22.9 Assume N Explain the difference between the quotient group (Z12 * Z4)/*

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Please write the statements of the questions more carefully (use words where you do not have or know formatting). In the first qestion something is missing after "then", then inZ is unclear and so is |/|. In the second question it seems a part is cut off ( what is "assume N"?), and the last part is unclear.

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I noticed that a part of the problem was that this application does not accept "less than" and "larger than" signs we use to denote subgroups through generators. The preview will tell you if some symbol does not go through - in that case please use words.

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Is there any old exams that are available to us?

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I'll try to find some tomorrow and post it (or them) on the web page. (I do not know if the math department has old exams in their files.)

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did you have any luck with the old exams?

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The math department has only one old 136.330 exam in the archives, and that particular exam is not suitable (most of the questions are "state the definition/theorem" - not the type of questions you will see in your exam). If you randomly choose 9 questions, one from chapter 1 and 2 from each of the chapters 2,3 and 4 and 5, you would get a much better approximation of your exam.