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\(n\)th root of unity, Paragraph
Abelian group, Paragraph
Euclidean, Paragraph
inner, Exercise
Binary operation, Paragraph
Burnside, William, 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
left, Paragraph
representative, Paragraph
right, Paragraph
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
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
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, √Čvariste, Paragraph
Generator of a cyclic subgroup, Definition
Generators for a group, Paragraph
Greatest common divisor
of two integers, Paragraph
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
canonical, Paragraph
kernel of a group, Paragraph
natural, Paragraph
of groups, Paragraph
Index of a subgroup, Paragraph
first principle of, Principle
second principle of, Principle
Internal direct product, Paragraph
of groups, Paragraph
of a group homomorphism, Paragraph
Klein, Felix, Paragraph
Lagrange's Theorem, Theorem
Lagrange, Joseph-Louis, Paragraph Paragraph Paragraph
Laplace, Pierre-Simon, Paragraph
Left regular representation, Paragraph
Lie, Sophus, Paragraph
Linear transformation
definition of, Example
Mapping, seeFunction
similar, Example
Normal subgroup, Paragraph
Partitions, Paragraph
definition of, Example Paragraph
even, Paragraph
odd, Paragraph
Permutation group, Paragraph
Prime integer, Paragraph
Primitive \(n\)th root of unity, Paragraph
Quaternions, Example
Rigid motion, Paragraph
Second Isomorphism Theorem
for groups, Theorem
cyclic, Definition
definition of, Paragraph
index of, Paragraph
normal, Paragraph
proper, Paragraph
trivial, Paragraph
Third Isomorphism Theorem
for groups, Theorem
Transposition, Paragraph
Well-defined map, Paragraph
Well-ordered set, Paragraph