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## Exhibit a group homomorphism on the Heisenberg group

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.11 Let $F$ be a field and let G = \left\{ \begin{bmatrix} a & b \\ 0…

## 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…

## Compute the center of a Heisenberg group

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.2 Exercise 2.2.14 Let $F$ be a field and let $H(F)$ denote the Heisenberg group over $F$ as defined…