Normal subgroups whose order and index are coprime are unique up to order
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.19 Let $G$ be a finite group, $N \leq G$ a normal subgroup, and suppose that $|N|$…
Finite subgroups with relatively prime orders intersect trivially
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.8 Let $G$ be a group and let $H, K \leq G$ be finite subgroups of relatively…