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Review title: A compact and Accessible Introduction to Infinite Group Theory
Product review: Kaplansky explicitly states in the forward that this book is not so much aimed at those wanting to learn about infinite abelian groups, but rather at those wanting to learn about infinite algebra. While this book is certainly a superb introduction to the theory of infinite abelian groups, it does a better job of teaching familiarity with the methods of proof commonly used in more advanced mathematics. As such, the book is extremely accessible, requiring only the absolute basics of group theory. On the other hand, it does require a certain level of "mathematical maturity," the ability to learn with a minimum of motivation and fill in gaps in proofs. For the specialist looking for a reference on infinite abelian groups, I would recommend both volumes of Laszlo Fuchs'Infinite Abelian Groups, Volume 1, Volume 36-I (Pure and Applied Mathematics), which is aimed more at the professional mathematician than the amature.
