Dummit and Foote Chapter 4 is challenging because it introduces a new language of symmetry. But with the right solutions as a scaffold—not a crutch—you will emerge with a powerful, intuitive grasp of group actions that will carry you through the rest of the book and into research-level algebra.
Let ( G ) act on a set ( A ). For ( a, b \in A ), prove that either ( \mathcalO_a = \mathcalO_b ) or ( \mathcalO_a \cap \mathcalO_b = \emptyset ). abstract algebra dummit and foote solutions chapter 4
