## 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…

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.4 Exercise 1.4.10 Let $G = \left\{ \left[{a \atop 0} {b \atop c}\right] \ |\ a,b,c \in \mathbb{R}, a…

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) = \{…

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.16 Let $n \in \mathbb{Z}^+$ and let $F$ be a field. Prove that the set $$UT_n(F) =…