Group theory proofs can be subtle. Use the Overleaf "Review" feature to share your work with classmates.
The exercises in 4.3 are "bread and butter" for exam prep. You will use the equation: dummit+and+foote+solutions+chapter+4+overleaf+full
Solutions to Chapter 4 of Dummit and Foote on Overleaf Group theory proofs can be subtle
\beginproof Write $A$ as a disjoint union of orbits. Each nontrivial orbit has size dividing $|G|$, hence divisible by $p$. Thus $|A| \equiv |\operatornameFix(G)| \pmodp$. \endproof dummit+and+foote+solutions+chapter+4+overleaf+full