A Course on Group Theory (Dover Books on Mathematics)
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I don't currently own a dedicated group theory book, and I think I'd find such a book very helpful in my research. What is your favorite book on group theory? Please tell us why you like it -- and what sort of groups it focuses on finite? For my part, I'm interested mainly in discrete, finitely generated groups, but I enjoy the "flavor" of general group theory books more than combinatorial group theory books. However, when I need info on the representation theory of these groups, I end up turning to Steinberg's lecture notes alas, not in print.
Another important reference here is Bass's book "Algebraic K-Theory". For arithmetic groups here there is some overlap with answer 3 , I like Dave Witte Morris's book on the subject it's not in print yet, but it is available on his webpage. For geometric group theory, in addition to the wonderful book of Bridson and Haefliger that Henry mentioned, I like Pierre de la Harpe's book on the subject mostly for the amazing bibliography. For the symmetric group, I really like G. Robinson's "A Course in the Theory of Groups" is a very good general group theory reference, with a rather extensive bibliography.
Serre's Trees has a nice treatment of Bass-Serre theory in the first chapter. This concerns infinite discrete groups. The book displays Serre's usual qualities of very concise writing and an eye for important points. Martin Issacs. It contains all the standard material one would expect in a graduate group theory text as well as a number of topics you don't normally see in such texts, like subnormality and the Chernoff measure. It's quite a bit more advanced than the usual group theory texts as well.
Collected Papers of Bertram Kostant: Volume IV 1989-1999
All of it is presented beautifully with Issacs' usual authority and scholarship. For older and more standard texts, there's always the old classic by Philip Hall. And, of course, there's always John S.
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