# hw11.pdf - MODERN ALGEBRA 1 HOMEWORK 11 Problem Classify...

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MODERN ALGEBRA 1: HOMEWORK 11 Problem. Classify all groups of order up to 30 up to isomorphism. You may skip orders 8, 16, 24, and 27. You may choose one of 12, 18, and 20, and skip the other two. Concretely, the problem asks you to make a list of groups of order up to 30 such that every group of order up to 30 is isomorphic to a unique member of the list. The groups of order 8, 16, 24, and 27 require some ingenuity beyond what we have done in class. You are free to attempt to classify them, but you don’t have to. The cases of orders 12, 18, and 20 are similar. Make sure you prove that your list is exhaustive and does not contain repetitions. If you skip some orders, make it clear at the outset, so that the reader is not confused. After having done the mathematics, think about the best way to write it up. One way is to simply go down the list numerically — order 1, order 2, order 3, order 4, etc — but you can save space and time, and help the reader by stating and proving some of the recurring
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• Fall '17
• jane smith

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