Group18

Facts about double cosets
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 4.1 Exercise 4.1.10 Let $G$ b...
The set of all group automorphisms of a fixed group is a group
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.20 Let $G$ b...
Every finite group of even order contains an element of order 2
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.31 Let $G$ b...
Compute the order of an element in a direct product of groups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.30 Let $A$ a...
A finite direct product of groups is a group under componentwise multiplication
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.28 Let $A$ a...
In a group, the set of powers of a fixed element is a subgroup
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.27 Let $G$ b...
Subsets of a group which are closed under multiplication and inversion are groups
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.26 Let $(G, ...
Powers distribute over products of commuting group elements
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.24 Let $G$ b...
Characterization of the order of powers of a group element
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.23 Let $G$ b...
Conjugation preserves order
Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.1 Exercise 1.1.22 Let $G$ b...