Books Recommendation for Special Group Theory Topics

Question

I am attending a lesson in this semester in Group Theory, in the following special topics. I know that there are similar posts, but in this post I specifically ask to recommend me a combination of well written books or notes, with plenty of worked examples in the following topics:

Group Action on Set and on Group (Permutation Representation, Orbits, Stabilizers, The Orbit-Stabilizer Lemma), Burnside 's Lemma, Transitive Group Action, Group Action by conjugation (normalizer, centralizer), Semidirect product of two groups, dihedral groups, Abelian Groups (Free Abelian Groups with finite rank, Torsion Free Abelian Group, Periodic Abelian Group), The Splitting Theorem in finite generated abelian groups, Sylow Theorems (the method of counting, cycle method), Simple Groups, Small Order Groups, Solvable Groups, Solvability of $S_n$.

PS: I asked for a book combination because I believe that one single book doesn't contain all these topics

Thank you in advance.

Answer 1

If you are looking for a book which contains a lot of examples I can recommend "A first course in Abstract Algebra" by J. Fraleigh. It has too much text and examples for my taste, but it might be worth to look into. You may look into it here: http://www.vgloop.com/f-/1422977427-302599.pdf it features most of the topics listed.

Another book I have found to suit my preferences better is "Abstract Algebra, Theory and applications" by T. Judson. It presents the same topics in a more precise way than Fraleigh, although It might have less examples. http://abstract.ups.edu/download/aata-20100827.pdf

Last but not least, you should try to get your hands on "Algebra" by S. Lang. Although a bit more complicated than the previous two, but I suggest you should look into them.

Answer 2

Two classic books that contain all the topics listed in your question are:

Robinson, Derek John Scott A course in the theory of groups. Graduate Texts in Mathematics, 80. Springer-Verlag, New York-Berlin, 1982.

Rotman, Joseph J. An introduction to the theory of groups. Fourth edition. Graduate Texts in Mathematics, 148. Springer-Verlag, New York, 1995.

I add the book by Thomas W. Judson Abstract Algebra Theory and Applications available online here.

A good introduction, that I remembered, are the two books by Thomas W. Hungerford for which I studied abstract algebra. The first is very elementary is suitable for anyone who has never seen groups in their life. Abstract Algebra. The second is Algebra. Suitable for anyone who has already had a first group theory course.

Answer 3

Actually, I know two books, such that each of them contains all those topics (and also many additional information regarding group theory). One of them is "Group Theory" by Alexander Kurosh (however, I do not know whether it is translated to English or not; the language of the original is Russian). The other one is "The Theory of Groups" by Marshall Hall.

Answer 4

Well, actually I know a very good book that contains all of the topics that you have mentioned.That is Fundamentals Of Abstract Algebra by Malik, Mordeson,Sen. Really it is a very nice book to develop concept properly.Pdf is available in internet. Thank you.