My goal is to provide some help in reviewing Chapters 7 and 8 of our book Abstract Algebra. I have included summaries of most of these sections, together with some general comments. The review problems are intended to have relatively short answers, and to be more typical of exam questions than of standard textbook exercises.
By assuming that this is a review. I have been able make some minor changes in the order of presentation. The first section covers various examples of groups. In presenting these examples, I have introduced some concepts that are not studied until later in the text. I think it is helpful to have the examples collected in one spot, so that you can refer to them as you review.
A complete list of the definitions and theorems in the text can be found on the web site wu. math. niu. edu/^beachy/aaol/ . This site also has some group multiplication tables that aren't in the text. I should note two minor changes in notation-I've used 1 to denote the identity element of a group (instead of e). and I've used the abbreviation "iff" for "if and only if".
Abstract Algebra begins at the undergraduate level, but Chapters 7-9 are written at a level that we consider appropriate for a student who has spent the better part of a year learning abstract algebra. Although it is more sharply focused than the standard graduate level textbooks, and does not go into as much generality. I hope that its features make it a good place to learn about groups and Galois theory, or to review the basic definitions and theorems.
Finally, I would like to gratefully acknowledge the support of Northern Illinois University while writing this review. As part of the recognition as a "Presidential Teaching Professor." I was given leave in Spring 2000 to work on projects related to teaching.