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## 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.…

## Definition of the Heisenberg group over a field

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.11 Let $F$ be a field, and define the Heisenberg group $H(F)$ over, $F$ by (1) Show…