General Linear Group15

Exhibit symmetric group as a subgroup of a general linear group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.9 Solution: ...
The special linear group is normal in the general linear group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.35 Let $F$ b...
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...
2×2 invertible upper triangular matrices form a subgroup of general linear group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.10 Let $G = ...
General linear groups of dimension at least 2 are nonabelian
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.8 Show that ...
Computation of the order of the general linear group of index 2 over Z/(p)
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.7 Let $p$ be...
The order of a general linear group over a finite field is bounded above
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.6 Let $F$ be...
A general linear group over a field is finite if and only if the field is finite
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.5 Let $F$ be...
Show that a given general linear group is nonabelian
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.3 Show that ...
Compute the order of each element in the general linear group of dimension 2 over Z/(2)
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.2 Write out ...