Root of Unity6

In an integral domain, there are at most two square roots of 1
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.11 Prove tha...
The group of complex p-power roots of unity is a proper quotient of itself
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.3 Exercise 3.3.8 Let $p$ be...
Q/Z is isomorphic to the group of complex roots of unity
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.14 Consider ...
Compute the kernel and fibers of a given group homomorphism
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.13 Let $G$ b...
Represent the real numbers as complex numbers of modulus 1
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.12 Let $G$ b...
Surjective group endomorphisms need not be automorphisms
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.19 Let $G = ...