So I finished Lang's Algebra and after reading this partial Structure Theorem for abelian torsion groups that are not finitely generated , I've gotten interested in abelian groups, in particular infinite abelian groups and structure theorems. Can anyone recommend a book that highlights these topics?



Though I haven't read it myself, Kaplansky's book Infinite Abelian Groups seems like it is just right for you. Here are the contents:

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  • $\begingroup$ Hm, I just picked it up in the stacks. Seems short and sweet. Thanks! $\endgroup$ – Pax Kivimae Jul 23 '13 at 22:36

A more in-depth, and therefore substantially longer, book is Fuch's Abelian Groups. I won't paste in the contents, as they run to three pages!

I notice that the review of Kaplansky's book refers the reader to Fuch's Infinite Abelian Groups, Vol I and II. These are more modern than Abelian Groups, published in 1973 I believe as opposed to 1960. However, Abelian Groups can be picked up for 9.00 Dollars as opposed to 34.31 Dollars (Vol. I) + 186.06 Dollars (Vol. II) = a lot more than 9 Dollars.

  • $\begingroup$ Ironically, I found Fuch right next to Kapalnsky in the stacks, and picked it up after remembering the name in the last section. Thanks for affirming that I should read it! $\endgroup$ – Pax Kivimae Jul 25 '13 at 16:21

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