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## 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.…