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.
please provide your suggestions. thanks
Solution 1:
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.
Solution 2:
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:
Problems in Group Theory - Dixon
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.