13.3: Reading Questions
How many abelian groups are there of order \(200 = 2^3 5^2\text{?}\)
How many abelian groups are there of order \(729=3^6\text{?}\)
Find a subgroup of order 6 in \(\mathbb Z_8\times\mathbb Z_3\times\mathbb Z_3\text{.}\)
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?
What is a principal series of the group \(G\text{?}\) Your answer should not use new terms defined in this chapter.