In need of a group theory textbook.

Question

I am in need of a group theory textbook for a good summer review. I have already studied from various books (mostly "group theory" part from basic algebra books) and the lecture notes of my teacher, but these notes lack any rigour and are incomplete, while I still have to find a book that can cover all that I've been taught in a way that attracts me. For that reason, any recommendation on group theory books, or online lecture notes would be really appreciated.
The material that we covered in class was:
a) actions on groups
b) sylow theorems and applications
c) (semi)products and applications
d) series, solvability, nilpotency
e) introduction to free groups

Thanks a lot in advance.

This book treats group actions, sylows and series, solvablity with very detail and lots of examples and exercises. Although it does not touch free groups , nilpotency and semi direct product. For those topics, you can consult Rotmans book, but I found semidirect product treated more comprehensibly in Dummit and Foote — Bhaskar Vashishth, Jul 03 '15 at 18:22
Does this answer your question? What is a good book for a second "course" in group theory? — , May 30 '23 at 05:38

vasmous · Accepted Answer · 2015-07-03T19:16:21.293

Although I believe that Dummit and Foote's Abstract Algebra combined with Herstein's Topics in Algebra which has excellent exercises is the perfect recipe for the job, I would recommend two more books for the study of finite groups. The first one is Daniel Gorenstein's Finite Groups which is a book of great depth and covers a lot of material about groups. The second one is William Burnside's Theory of Groups of Finite Order (it is available for free).
Some classmates of mine mentioned this book by M. Aschbacher but I have never used it.
I hope that I helped you!

EDIT: I almost forgot. Perhaps the most elegant notes ever written on this subject Group Theory - J.S. Milne.

score 4 · Answer 2 · answered Jul 03 '15 at 18:07

4

Try these excellent books:

An Introduction to the Theory of Groups by Rotman.
The Theory of Groups by Marshall Hall Jr.

answered Jul 03 '15 at 18:07

lhf

221,500

score 1 · Answer 3 · answered Jul 03 '15 at 18:08

1

I enjoyed Michael Artin's book Algebra. This would still be as you say the "group theory" part of an abstract algebra book, but it is rigorous and touches on the topics you have listed.

answered Jul 03 '15 at 18:08

TomGrubb

13,177

score 1 · Answer 4 · answered Jul 03 '15 at 18:41

1

Martin Isaac's book Algebra might be useful to you. It is at the graduate level so it might be useful if you are going through the material a second time.

answered Jul 03 '15 at 18:41

abnry

14,976

In need of a group theory textbook.

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