The Theory of Finite Groups: An Introduction

I don't think I could come up with enough superlatives to describe just how good this text really is. Both authors have done an excellent job describing as well as motivating the subject and have subsequently turned me into an avid fan of the theory of finite groups. What I find disappointing is my assumption that the available pool of readers is more like a shallow puddle. This can easily be seen from the fact that, as thriving of a subject finite groups may be, it does not appear in the course catalog of most academic institutions. It would be nice to see this book adopted as a seniors honor course for undergraduates or as an advanced algebra course for graduate students looking to specialize in matters algebraic. Now, off my soap box. Without a doubt this text will become another classic in the field of finite groups, akin to Gorenstein's. So who can read this text? Well, as un-original as it is, the mathematically mature and, more importantly, anyone who has taken an Algebra course that covered the standard basics of group theory. To be exact, if you learned Algebra using Hungerford's text, then you should be adequately prepared for this book. Of course this assumes you have seen and understand the how's/why's of the Sylow theorems, the structure and purpose of Abelian groups, the role Normality plays and, in my opinion, you should have a firm grasp of the role/structure/purpose of the various types of morphisms (homomorphism, epimorphism, monomorphism, and isomorphism)and how and why they are so important in group theory. The only drawback to this book is that the exercises seemingly disappear after page 223 in the chapter dealing with groups acting on groups. I know the material becomes more dense, more difficult and more abstract but, I would have assumed that the authors could have provided the reader with exercises post chapter 8 (even if the exercise was finishing a proof). Aside from that, I would recommend this text to everyone and anyone. In particular, if you are not a math wiz and just plain interested in learning about finite groups, then I would suggest that you pick up this text. Good luck and happy proving!