The Theory of Groups 2nd Edition by Hans J. Zassenhaus (PDF)

Description

Group theory represents one of the most fundamental elements of mathematics. Indispensable in nearly every branch of the field, concepts from the theory of groups also have important applications beyond mathematics, in such areas as quantum mechanics and crystallography.Hans J. Zassenhaus, a pioneer in the study of group theory, has designed this useful, well-written, graduate-level text to acquaint the reader with group-theoretic methods and to demonstrate their usefulness as tools in the solution of mathematical and physical problems. Starting with an exposition of the fundamental concepts of group theory, including an investigation of axioms, the calculus of complexes, and a theorem of Frobenius, the author moves on to a detailed investigation of the concept of homomorphic mapping, along with an examination of the structure and construction of composite groups from simple components. The elements of the theory of p-groups receive a coherent treatment, and the volume concludes with an explanation of a method by which solvable factor groups may be split off from a finite group.Many of the proofs in the text are shorter and more transparent than the usual, older ones, and a series of helpful appendixes presents material new to this edition. This material includes an account of the connections between lattice theory and group theory, and many advanced exercises illustrating both lattice-theoretical ideas and the extension of group-theoretical concepts to multiplicative domains.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I’m not always quick on the update, so I’ve struggled with this book. I think the text is reasonably clear, if a little dense. The real issue is the typography — it’s relatively small print and clearly not written using modern technology. This is the 2nd edition, published in 1999, but I’m not sure how much it was actually revised from the original 1970’s text. I’m not sure I can recommend it, though I haven’t found a better alternative that costs less than my monthly car payment.

⭐Zassenhaus was an important figure in the development of Group Theory, and there is value in seeing the development in its original form. Maybe not a book for a math student with a heavy course load. Another reviewer said the symbol conventions have changed. Also, this is not a “first course” at all, and assumes familarity with matrices, combinatorics, and more, and is written in a very concise, non-explanatory way, This would be at least a senior level math undergraduate “math major” text (the cover says graduate level). I am familiar with the Greek alphabet, but not sure about those bold-face gothic Russian-looking letters that look like Chinese characters. I’m looking forward to working my way through it, because of how the development is structured, but will definitely be referring to other sources that explain the prerequisite concepts in more detail.

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