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Reading Questions 13.3 Reading Questions
1.
How many abelian groups are there of order \(200 = 2^3 5^2\text{?}\)
2.
How many abelian groups are there of order \(729=3^6\text{?}\)
3.
Find a subgroup of order 6 in \(\mathbb Z_8\times\mathbb Z_3\times\mathbb Z_3\text{.}\)
4.
It can be shown that an abelian group of order \(72\) contains a subgroup of order \(8\text{.}\) What are the possibilities for this subgroup?
5.
What is a principal series of the group \(G\text{?}\) Your answer should not use new terms defined in this chapter.
