# IndexIndex

\(n\)th root of unity, Paragraph

Cancellation law

for groups, Paragraph

Cauchy, Augustin-Louis, Paragraph

Cayley table, Paragraph

Cayley's Theorem, Theorem

Cayley, Arthur, Paragraph

Commutative diagrams, Paragraph

Composite integer, Paragraph

Congruence modulo \(n\), Example

Conjugate, complex, Paragraph

Correspondence Theorem

for groups, Theorem

Coset

left, Paragraph

representative, Paragraph

right, Paragraph

Cycle

definition of, Paragraph

disjoint, Paragraph

De Morgan's laws

for sets, Theorem

DeMoivre's Theorem, Theorem

Direct product of groups

external, Paragraph

internal, Paragraph

Division algorithm

for integers, Theorem

Element

identity, Item

inverse, Item

order of, Paragraph

Equivalence class, Paragraph

Equivalence relation, Paragraph

Euclidean algorithm, Paragraph

Euler \(\phi\)-function, Paragraph

Euler, Leonhard, Paragraph

External direct product, Paragraph

Fermat's Little Theorem, Theorem

Fermat, Pierre de, Paragraph

Finitely generated group, Paragraph

First Isomorphism Theorem

for groups, Theorem

Function

bijective, Paragraph

composition of, Paragraph

definition of, Paragraph

domain of, Paragraph

identity, Paragraph

injective, Paragraph

invertible, Paragraph

one-to-one, Paragraph

onto, Paragraph

range of, Paragraph

surjective, Paragraph

Fundamental Theorem

of Arithmetic, Theorem

of Finite Abelian Groups, Theorem

Galois, Évariste, Paragraph

Generator of a cyclic subgroup, Definition

Generators for a group, Paragraph

Greatest common divisor

of two integers, Paragraph

Group

abelian, Paragraph

alternating, Paragraph

circle, Paragraph

commutative, Paragraph

cyclic, Definition

definition of, Paragraph

dihedral, Paragraph

factor, Paragraph

finite, Paragraph

finitely generated, Paragraph

general linear, Example

generators of, Paragraph

homomorphism of, Paragraph

infinite, Paragraph

isomorphic, Paragraph

isomorphism of, Paragraph

nonabelian, Paragraph

noncommutative, Paragraph

of units, Example

order of, Paragraph

permutation, Paragraph

quaternion, Example

quotient, Paragraph

special linear, Example

symmetric, Paragraph

Group\(p\)-group, Paragraph

Homomorphic image, Paragraph

Homomorphism

canonical, Paragraph

kernel of a group, Paragraph

natural, Paragraph

of groups, Paragraph

Index of a subgroup, Paragraph

Induction

first principle of, Principle

second principle of, Principle

Internal direct product, Paragraph

Isomorphism

of groups, Paragraph

Lagrange's Theorem, Theorem

Laplace, Pierre-Simon, Paragraph

Left regular representation, Paragraph

Lie, Sophus, Paragraph

Linear transformation

definition of, Example

Normal subgroup, Paragraph

Partitions, Paragraph

Permutation

even, Paragraph

odd, Paragraph

Permutation group, Paragraph

Prime integer, Paragraph

Primitive \(n\)th root of unity, Paragraph

Quaternions, Example

Rigid motion, Paragraph