Abelian Group32

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:...
Every abelian simple group has prime order
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.4 Exercise 3.4.1 Solution: ...
The center of a direct product is the direct product of the centers
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.1 Show that ...
An abelian group has the same cardinality as any sets on which it acts transitively
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.3 Suppose $G...
The intersection by an abelian normal subgroup is normal in the product
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.20 Let $G$ b...
A finite group of width two has a trivial center
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.4 Let $G$ be...
The set of all endomorphisms of an abelian group is a ring under pointwise addition and composition
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.29 Let $A$ b...
Q/Z is divisible
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.15 Prove tha...
Every quotient of an abelian group is abelian
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.3 Let $A$ be...
Additive subgroups of the rationals which are closed under inversion are trivial
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.1 Exercise 2.1.13 Let $H$ b...