Permissible subgroup orders in a group of order 120, and their indices
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.1 Which of the following are permissible orders for subgroups of a group of order 120: 1,…
The order of conductor f in the ring of quadratic integers is a subring and has index f
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.23 Let $D$ be a squarefree integer, and let $O$ be the ring of integers in the…
A fact on the interaction of subgroups with subgroups of prime index
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.3 Let $G$ be a group, $N \leq G$ a normal subgroup of prime index $p$, and…
Compute the index of the special linear group in the general linear group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.1 Let $F$ be a finite field of order $q$ and let $n$ be a positive integer.…
- 1
- 2