Chapter 11

Exercise 1. This software lists the isomorphism classes of all finite Abelian groups of order n. Assume that n < 1,000,000. Run your program for n = 16, 24, 512, 2048, 441000, and 999999.

Exercise 2. This software determines how many integers in a given interval are the order of exactly one Abelian group, of exactly two Abelian groups, and so on, up to exactly nine Abelian groups. Run your program for the integers up to 1000. Then from 10001 to 11000. Then choose your own interval of 1000 consecutive integers. Is there much difference in the results?

Exercise 3. This software expresses U-groups as internal direct product of subgroups H₁ X H₂ X ... X H_t, where |H_i| divides |H_{i -1|} . Run your program for the groups U(32), U(80), and U(65).

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