Abstract Algebra, Third Edition I. N. Herstein

 Abstract Algebra, Third Edition I. N. Herstein

      It has been pointed out to us that some instructors would find it useful to have the Symmetric Group Sn and the cycle notation available in Chapter 2, in order to provide more examples of groups. Rather than alter the arrangement ofthe 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 offinite 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.

Topics are discussed in this book are

1 Things Familiar and Less Familiar

2 Groups

3 TheSymmetric Group

4 RingTheory

5 Fields

 6.Special Topics (Optional)

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