$\newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{\nmid} \newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}} \newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}} \newcommand{\Null}{\operatorname{Null}} \newcommand{\transpose}{\text{t}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \setcounter{chapter}{-1}$

# IndexIndex

$n$th root of unity
Abelian group
Algorithm
Euclidean
Automorphism
inner
Binary operation
Burnside, William
Cancellation law
for groups
Cauchy, Augustin-Louis
Cayley table
Cayley's Theorem
Cayley, Arthur
Commutative diagrams
Composite integer
Congruence modulo $n$
Conjugate, complex
Correspondence Theorem
for groups
Coset
left
representative
right
Cycle
definition of
disjoint
De Morgan's laws
for sets
DeMoivre's Theorem
Direct product of groups
external
internal
Division algorithm
for integers
Element
identity, Item
inverse, Item
order of
Equivalence class
Equivalence relation
Euclidean algorithm
Euler $\phi$-function
Euler, Leonhard
External direct product
Fermat's Little Theorem
Fermat, Pierre de
Finitely generated group
First Isomorphism Theorem
for groups
Function
bijective
composition of
definition of
domain of
identity
injective
invertible
one-to-one
onto
range of
surjective
Fundamental Theorem
of Arithmetic
of Finite Abelian Groups
Galois, Évariste
Generator of a cyclic subgroup
Generators for a group
Greatest common divisor
of two integers
Group
abelian
alternating
circle
commutative
cyclic
definition of
dihedral
factor
finite
finitely generated
general linear
generators of
homomorphism of
infinite
isomorphic
isomorphism of
nonabelian
noncommutative
of units
order of
permutation
quaternion
quotient
special linear
symmetric
Group$p$-group
Homomorphic image
Homomorphism
canonical
kernel of a group
natural
of groups
Index of a subgroup
Induction
first principle of
second principle of
Internal direct product
Isomorphism
of groups
Kernel
of a group homomorphism
Klein, Felix
Lagrange's Theorem
Lagrange, Joseph-Louis
Laplace, Pierre-Simon
Left regular representation
Lie, Sophus
Linear transformation
definition of
Mapping, seeFunction
Matrix
similar
Normal subgroup
Partitions
Permutation
definition of
even
odd
Permutation group
Prime integer
Primitive $n$th root of unity
Quaternions
Rigid motion
Second Isomorphism Theorem
for groups
Subgroup
cyclic
definition of
index of
normal
proper
trivial
Third Isomorphism Theorem
for groups
Transposition
Well-defined map
Well-ordered set