Cyclic Group30

Find a generating set for the augmentation ideal of a group ring
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.4 Exercise 7.4.2 Solution: ...
Compute presentations for a given central product of groups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.13 Solution:...
Basic properties of the central product of groups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.12 Solution:...
Exhibit the distinct cyclic subgroups of an elementary abelian group of order $p^2$
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.10 Solution:...
Exhibit a group homomorphism from Z/(8) to Z/(4)
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.10 Let $\var...
Characterize the automorphisms of cyclic group of order n
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.26 Let $Z_n ...
Characterize the normalizer of a cyclic subgroup
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.24 Let $G$ b...
The group of units in $\mathbb Z/(2^n)$ is not cyclic for n at least 3
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.23 Show that...
Unique group homomorphism from Z to any group where the image of 1 is fixed
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.19 Show that...
Group homomorphism from cyclic group is determined by the image of generator
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.18 We write ...