Présentation de la Collection : Mathématiques pour le deuxième cycle
When we were asked to prepare the third edition of this book, it was our consensus that it should not be altered in any significant way, and that Herstein's informal style should be preserved. We feel that one of the book's virtues is the fact that it covers a big chunk of abstract algebra in a condensed and interesting way. At the same time, without trivializing the subject, it remains accessible to most undergraduates.
We have, however, corrected minor errors, straightened out inconsistencies, clarified and expanded some proofs, and added a few examples.
To resolve the many typographical problems of the second edition, Prentice Hall has had the book completely retypeset making it easier and more pleasurable to read.
It has been pointed out to us that some instructors would find it useful to have the Symmetric Group S„ and the cycle notation available in Chapter 2, in order to provide more examples of groups. Rather than alter the arrangement of the contents, thereby disturbing the original balance, we suggest an alternate route through the material, which addresses this concern.
After Section 2.5, one could spend an hour discussing permutations and their cycle decomposition (Sections 3.1 and 3.2), leaving the proofs until later.
The students might then go over several past examples of finite groups and explicitly set up isomorphisms with subgroups of Sn. This exercise would be motivated by Cayley's theorem, quoted in Section 2.5. At the same time, it would have the beneficial result of making the students more comfortable with the concept of an isomorphism. The instructor could then weave in the various subgroups of the Symmetric Groups Sn as examples throughout the remainder of Chapter 2. If desired, one could even introduce Sections 3.1 and 3.2 after Section 2.3 or 2.4.
Two changes in the format have been made since the first edition. First, a Symbol List has been included to facilitate keeping track of terminology. Second, a few problems have been marked with an asterisk (*). These serve as a vehicle to introduce concepts and simple arguments that relate in some important way to the discussion. As such, they should be read carefully.
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