Kernel18

Prove that a given function is a ring homomorphism and describe its kernel
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.7 Solution: ...
Computation of all ring homomorphisms from Z to Z/(30)
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.4 Find all r...
Generalized coordinate subgroups of a direct product
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.2 Solution: ...
Stabilizer commutes with conjugation II
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.2 Let $G$ be...
Stabilizer commutes with conjugation
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.1 Solution: ...
Compute the kernel of the left regular action of a group on itself
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.13 Find the ...
A group action is faithful precisely when the kernel of the corresponding permutation representation is trivial
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.6 Prove that...
The kernel of a group action is precisely the kernel of the induced permutation representation
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.5 Prove that...
The kernel and stabilizers of a group action are subgroups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.4 Let $G$ be...
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 $F$ b...