Order37

A finite group of composite order n having a subgroup of every order dividing n is not simple
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.14 Solution:...
If a group has order 2k where k is odd, then it has a subgroup of index 2
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.2 Exercise 4.2.13 Solution:...
Conjugation by a fixed group element is an automorphism
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.7 Exercise 1.7.17 Let $G$ b...
Perform explicit computation in a quotient of the modular group of order 16
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.19 Let $G = ...
Perform explicit computation in a quotient of a quasi-dihedral group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.18 Let $G = ...
Compute the order of a quotient group element
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 3.1 Exercise 3.1.5 Let $G$ be...
Compute the order of 5 in the integers mod a power of 2
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.22 Let $n$ b...
Use the Binomial Theorem to compute the order of an element in the integers mod a prime power
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.21 Let $p$ b...
If a prime power power of a group element is trivial, then the order of the element is a prime power
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.20 Let $p$ b...
The order of a product of commuting group elements divides the least common multiple of the orders of the elements
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 2.3 Exercise 2.3.16 Let $G$ b...