Prime Number7

Count the number of cyclic subgroups in an elementary abelian p-group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.11 Solution:...
The Sylow numbers of a direct product are products of the Sylow numbers
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 5.1 Exercise 5.1.4 Solution: ...
An example of a nilpotent ideal
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.37 Solution:...
The characteristic of an integral domain is prime or zero
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.3 Exercise 7.3.28 Solution:...
n divides the totient of $p^n-1$ when p is prime
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.15 Let $p$ b...
Alternate proof of Cauchy’s Theorem
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.2 Exercise 3.2.9 Solution: ...
Examples of nilpotent elements
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 7.1 Exercise 7.1.13 An elemen...