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 $F$ be a field and $n$ a positive integer. Prove that $SL_n(F)$ is normal in…
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.…
Set of all strictly upper triangular matrices is a subgroup of general linear group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.17 Let $n \in \mathbb{Z}^+$ and let $F$ be a field.Prove that the set $$UT_n^1(F) = \{…
Special linear group is a subgroup of general linear group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.9 Let $F$ be a field and define $SL_n(F) \subseteq GL_n(F)$ by $$SL_n(F) = \{ A \in…