User:Jshflynn/Hungerford Algebra

$\S 1.1$
Definition:Operation/Binary Operation

Definition:Operation/Binary Operation/Product

Definition:Semigroup

Definition:Monoid

Definition:Group

Definition:Abelian Group

Definition:Order of Structure

Definition:Finite Group

Definition:Infinite Group

Identity is Unique

Identity Only Idempotent Element in Group

Cancellation Laws

Inverses in Monoid are Unique

Inverse of Inverse/Group

Inverse of Product/Group

Equivalence of Axiom Schemata for Groups

Equivalence of Axiom Schemata for Groups

Integers Infinite Cyclic Group

Additive Group of Rational Numbers

Additive Group of Real Numbers

Integer Multiplication forms Commutative Monoid

Rational Multiplication forms Commutative Monoid

Multiplicative Group of Rational Numbers

Multiplicative Group of Real Numbers

Definition:Symmetry Group

Symmetry Group is Group

Group of Permutations is Group

Definition:Permutation on n Letters

Definition:Symmetric Group

Symmetric Group is Group

Order of Symmetric Group

Definition:Group Direct Product

Group Direct Product is Group

Group Direct Product of Abelian Groups

Definition:Congruence Relation

Quotient Structure is Well-Defined

Definition:Integers Modulo m

Additive Group of Integers Modulo m

Multiplicative Group of Integers Modulo m

Definition:Meaningful Product

Definition:Standard n Product

General Associativity Theorem

General Commutativity Theorem

Definition:Power of Element/Semigroup

Definition:Power of Element/Monoid

Definition:Power of Element/Group

Index Laws for Monoids/Sum of Indices

Index Laws for Monoids/Product of Indices

Mappings to Algebraic Structure form Similar Algebraic Structure

Equivalence of Axiom Schemata for Groups/Warning

Order of Symmetric Group

Definition:Klein Four-Group

Boolean Group is Abelian

Even Order Group has Order 2 Element