Abstract Algebra MOC

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#MOC

Here are my lecture notes for when I took the class:

File	Type
19 - The Class Equation	Lecture Notes
18 - Cayley Theorem	Lecture Notes
17 - Finishing the Isomorphism Theorems	Lecture Notes
16 - The Four Horsemen Theorems	Lecture Notes
15 Cosets and Usage of Lagrange's Theorem	Lecture Notes
14 Lagrange's Theorem	Lecture Notes
13 Quotient Groups (cont.)	Lecture Notes
12 Quotient Groups	Lecture Notes
11 - Setup for Group Morphisms	Lecture Notes
10 - Midterm Review	Lecture Notes
09 - Working with the -izers	Lecture Notes
08 - Centralizers, Normalizers, and Stabilizers	Lecture Notes
06 - Group Actions	Lecture Notes
07 - Subgroups	Lecture Notes
05 - Homomorphisms and Isomorphisms	Lecture Notes
04 - Families of Groups	Lecture Notes
03 - Dihedral Groups	Lecture Notes
02 - Properties of Groups	Lecture Notes
01 - Intro to the Course, Magma and Groups	Lecture Notes

And here are the concepts covered by topic:

File	Section, Subsection
Abelian Group	Definitions
Automorphisms	Definitions
Cancellation Theorem	Theorems
Cayley's Theorem	Theorems
Center	Definitions
Centralizer	Definitions
Common Findings of Homomorphisms	Theorems
Conjugacy Classes	Definitions
Conjugation Subgroup	Examples
Coset Conjoinment and Theorem	Theorems
Coset Product	Definitions
Cycle and Cycle Decomposition	Definitions
Cyclic Group	Definitions
Cyclic Groups of the Same Order are Isomorphic	Theorems
Cyclic Subgroups Z mod nZ	Examples
Description of Homomorphisms	Theorems
Dihedral Groups	Examples
Divisibility	Definitions
Equivalence for Transitive Group Actions	Theorems
Equivalences for Normal Subgroups	Theorems
Equivalences of Acting on Collections of Subgroups by Conjugation	Theorems
Equivalences of Group Actions	Theorems
Euler-Totient Function	Definitions
Faithful Action	Definitions
Fiber (Group Theory)	Definitions
Finite Groups, Order of x divides Order of G	Theorems
Fixing Subgroup	Definitions
Greatest Common Divisor	Theorems
Group	Definitions
Group Action	Definitions
Groups	Definitions
Homomorphism (or Group Morphism)	Definitions
Identity Element is Unique	Theorems
Index (Groups)	Definitions
Inverse Operation Distributes in Groups	Theorems
Isomorphism	Definitions
Kernel	Definitions
Lagrange's Divisibility Theorem of Order of Subgroups	Theorems
Left (and Right) Cosets form a Partition in G	Theorems
Left (and Right) Cosets form a Subgroup	Theorems
Left and Right Cosets	Definitions
Left Regular Representation	Definitions
Lemmas and Closure of Cosets	Theorems
Lemmas of Fixing Subgroups	Theorems
Magma (Algebraic)	Definitions
Matrix Groups	Examples
Normal Subgroup	Definitions
Normalizer	Definitions
Orbit	Definitions
Orbit Stabilizer Theorem	Theorems
Order (Groups)	Definitions
Orders of Cyclic Subgroups	Theorems
Paul's Theorem	Theorems
Prime Order Groups are Cyclic and Z_p	Theorems
Properties of Quotient Groups	Theorems
Properties of the Integers (Basic Number Theory)	0 Prerequisites
Quaternion Group	Examples
Quotient Group	Definitions
Reasoning Example for Quotient Group Definitions	Examples
Stabilizers	Definitions
Stabilizers are Subgroups	Theorems
Subgroup	Definitions
Subgroup Generator	Definitions
Symmetric Group & Permutations	Definitions
The Class Equation	Theorems
The First Isomorphism Theorem of Groups, The Fundamental Theorem for Group Morphisms	Theorems
The Fourth Isomorphism Theorem (The Lattice Isomorphism Theorem)	Theorems
The GCD of any two orders is the same order	Theorems
The Order of S_n is n!	Theorems
The Second Isomorphism Theorem (The Diamond Iso. Theorem)	Theorems
The Third Isomorphism Theorem (The Double Fraction Theorem)	Theorems
Transitive (Group Action)	Definitions
Trivial Group Action	Definitions
Unique Inverses	Theorems
Well Ordering of Z	Theorems
Z over nZ - The Integers Modulo n	0 Prerequisites