Full Solutions to exercises in Abstract Algebra: Theory and Applications by Thomas W. Judson (2021 Edition):
Chapter 3. Groups
Chapter 4. Cyclic Groups
Chapter 5. Permutation Groups
Chapter 6. Cosets and Lagrange’s Theorem
Chapter 9. Isomorphisms
Chapter 10. Normal Subgroups and Factor Groups
Chapter 11. Homomorphisms
Chapter 12. Matrix Groups and Symmetry
Chapter 13. The Structure of Groups
Chapter 14. Group Actions
Chapter 15. The Sylow Theorems
Abstract Algebra: Theory and Applications is the textbook I used to learn group theory in university. I will be posting my full solutions to exercises from this textbook as a resource for mathematics students. The book itself includes hints and answers to only a small number of exercises. I am really looking forward to diving back into this beautiful subject and sharing my journey with others. The author, Thomas W. Judson, has chosen to make the textbook available for free online. It can be downloaded here: https://judsonbooks.org/aata/
Abstract algebra is a beautiful and elegant branch of pure mathematics that includes studies such as group theory and ring theory. In abstract algebra you study “algebraic structures” by generalizing them and then studying their properties. Examples of algebraic structures include the integers, the real numbers, the symmetries of a square, the set of 2×2 invertible matrices, and the set of permutations of n objects.