problem book on Group theory after doing Fraleigh.

Please refer a problem book on

Group Theory:TOPICS: Groups, subgroups, Abelian groups, non-abelian groups, cyclic groups, permutation groups; Normal subgroups, Lagrange's Theorem for finite groups, group homomorphisms and basic concepts of quotient groups (only group theory).

I have already done A first course in abstract algebra by John b. Fraleigh. But I need one problem book to solve in order to be confident. I don't need a proof oriented problem book,my focus is to solve problems which are applications of theorems. I had Gallian on my mind, but it lacked solutions.

The best problems on group theory for a beginner, to me, is still contained in the second chapter of I.N.Herstien's Topics in Algebra. This is the book I learned algebra from and it still has the best exercises of any textbook I've seen. This is the book you want,trust me.

• Herstein's Topics in algebra is a great book. The starred and double starred problems are simply amazing. They help you "discover" algebra on your own and enjoy the learning.
– user348749
Aug 19, 2016 at 8:44

The book Contemporary Abstract Algebra by Joseph Gallian contains large number of problems with increasing order of difficulty.

For some advanced problems, one may refer to two problem books in group theory:

1. Problems in Group Theory - Dixon

2. Group Theory: Selected problems - B. Sury.

Another book on Group Theory with selected problems is "Groups and Representations: Alperin and Bell". It contains nice selected problems. However, the author(s) of the book say in the preface that the problems are unordered according to difficulty, with some philosophical thought.

• @singularity I also would have recommended Alperin/Bell,but I thought it was too sophisticated for you. Feb 23, 2015 at 21:04

Have a look into Problems in Group Theory - John Dixon (Dover ed.).

• I considered recommending Dixon,but I thought it was too sophisticated for what the OP was requesting. Feb 23, 2015 at 21:03
• Quality book for comprehensive exams. Jul 8, 2018 at 21:44

Algebra 3rd edition by Mac Lane and Birkhoff.

• Isn't this a rather old book?
– Pedro
Feb 23, 2015 at 8:44
• @PedroTamaroff, Algebra was very modern when it came out and it still has that feeling, but I'm biased since it was the first real algebra book I read. Perhaps you mean A Survey of Modern Algebra by Birkhoff and Mac Lane?
– lhf
Feb 23, 2015 at 10:40
• @lhf Yes, I think I'm confusing those. =)
– Pedro
Feb 23, 2015 at 10:54

You can also take a look into 'Algebra: a graduate course' and 'Finite group theory' both by I Martin Isaacs. Both are amazing books, I read the theory from the first book and solved problems from both books.