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A
- Application of Brauer's permutation lemma to group automorphisms on conjugacy class-representation duality
- Abelian
- Automorphism group of cyclic group of prime order
- Automorphism group of Zp for p prime is Z(p-1)
- Automorphism group of Cp for p prime is isomorphic to C(p-1)
- Automorphism groups
- All groups of order n are abelian if and only if n is cube free and no prime power dividing n is congruent to 1 mod a prime dividing n
- Abelian number
- Abelian-forcing number
- Agemo and omega subgroups
- Agemo and omega subgroups of a p-group
- Ableian implies nilpotent
- Abelian group:Z4XZ2
- Alternating group:A2
- Alternating group:A1
- Additive group of integers
B
- Book:Alperinbell
- Book:AlperinBell
- Book:DummitFoote
- Book:FGTAsch
- Book:Gorenstein
- Book:Herstein
- Book:Hungerford
- Book:Lang
- Book:MSYComb
- Book:Munkres
- Book:RobinsonAA
- Book:RobinsonGT
- Book:Schmidt
- B.H.Neumann's lemma
- Binary operations
- Basic definitions in linear representation theory
- Burnside’s theorem
C
- Compact space
- Classification of groups of order 2p
- Classification of group of order 12
- Classification of groups of order four times a prime congruent to 3 modulo four
- Classification of groups of order 4p
- Classification of groups of order 4 times a prime
- Completely reducible
- Cyclic group:C21
- Commutator subgroup of dihedral group
- Commutator subgroup of dihedral group is cyclic
- Commutators
- Commutator subgroup of abelian group
- Commutator subgroup of abelian group is trivial
- Commutator subgroup is trivial if and only if group is abelian
- Commutator subgroup of cyclic group
- Conjugacy classes
- Cyclic groups
- Classification of groups of order 2pq
- Classification of groups of order twice a product of two distinct primes
- Classification of groups of order twice a product of two distinct odd primes
- Class functions
- Character table equivalent groups
- Correspondence between normal subgroups and the character table of a finite group
- Character tables do not classify groups up to isomorphism
- Centre of dihedral group
- Classification of groups of prime squared order
- Classification of groups of order two times a prime
- Classification of groups of order p^5
- Classification of abelian numbers
- Classification of abelian-forcing numbers
- Classification of groups of order pqr
- Classification of groups of order product of three distinct primes
- Classification of groups of order 8p
- Classification of groups of order eight times a prime congruent to 3 mod 4
- Classification of groups of order eight times a prime congruent to 3 mod 8
- Classification of groups of order 16 times a prime
- Classification of groups of order 16p
- Classification of groups of order 32p
- Classification of groups of order 64p
- Classification of groups of order 128p
- Classification of groups of order 256p
- Classification of groups of order 512p
- Classification of groups of order 1024p
- Classification of groups of order one-thousand and twenty-four
- Classification of groups of order one-thousand and twenty-four times a prime
- Classification of groups of order pqrs
- C4xC2
- C4xc2
- C2xC2xC3
- C2xc2xc2
- Cyclic group of perfect number order is Leinster group
- Cyclic group is Leinster group if and only if perfect order
- Cyclic group is immaculate group if and only if of perfect order
- Cyclic group is immaculate group if and only if perfect order
- Cayley table
- Cubic field extension
- Complex representation of compact group is unitary
D
- Derived subgroup of abelian group
- Derived subgroups
- Dicyclic group:Dic16
- Direct products
- Dimension of irreducible representation divides order of group
- D10
- Dicyclic group:Dic32
- Dicyclic group:Dic64
- Dicyclic group:Dic128
- Dicyclic group:Dic256
- Dicyclic group:Dic512
- Dicyclic group:Dic1024
- Dicyclic group:Dic2048
- Dicyclic group:Dic4096
- Dicyclic group:Dic8192
- Dicyclic group:Dic16384
- Dicyclic group:Dic32768
- D8xZ2
- Dic36
- Direct product of S4 and S3
- Direct product of GL(2,3) and S3
- Direct product of Z7 and Z8
- Direct product of abelian groups is abelian
- Dual linear representation
E
- Element structure of M16
- Euler-phi function is multiplicative if coprime
- Elementary Abelian group:E8
- Erdos
- Erdős
- Endomorphism structure of the trivial group
- Endomorphism structure of trivial group
F
- Frobenius group: Z7⋊Z3
- Frobenius group of order 21
- Faithful representation
- Finite group with faithful irreducible representation over algebraically closed field has cyclic center
- Finite group with faithful irreducible representation over algebraically closed field has cyclic centre
- Frobenius reciprocity theorem
- Field of five elements
- Field automorphism
- Field homomorphism
- Field endomorphism
G
- Groups of order 4p
- Group representation
- Groups
- Group of order 16
- Galois extension
- Gnu function
- Groups of order n are abelian if and only if n is cube free and no prime power dividing n is congruent to 1 mod a prime dividing n
- Groups of order n are all abelian if and only if n is cube free and no prime power dividing n is congruent to 1 mod a prime dividing n
- General affine group:GA(1,4)
- General affine group:GA(1,2)
- General affine group:GA(1,3)
- Generalised quaternion group:Q16
- Groups of order 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
- Groups of order equal to the order of the monster group
- Groups of prime order
- Group of order n has minimal generating set of size at most log n
- Group of order n has minimal generating set of size at most log base 2 of n
- Group of order n has minimal generating set of size at most log base two of n
- GL(1,3)
- General linear group:GL(1,3)
- General linear group:GL(1,4)
- Generalised quaternion group:Q64
- Generalised quaternion group:Q32
- Generalised quaternion group
- GL(2,7)
- GL(2,9)
- GL(2,8)
H
I
- Inner product
- Irreducible character
- Irreducible representation of dimension greater than 1 will have character equal to zero on some conjugacy class
- Irreducible representation of dimension greater than one will have character equal to zero on some element
- Irreducible representation of dimension greater than 1 will have character equal to zero on some element
K
- Klein four group
- Kernel of representation is set of elements where the character evaluates to dimension of representation
L
- Linear representation theory of M16
- Linear representations
- Lagranges theorem
- Linear representation theory of Q8
- Linear representation theory of quaternion group:Q8
- Linear representation theory of D10
- Linear representation theory of cyclic group:Z1
- Linear representation theory of general affine group:GA(1,4)
- Linear representation theory of general affine group:GA(1,3)
- Linear representation theory of general affine group:GA(1,2)
- Linear representation theory of SU(2)
- Linear representation theory of special unitary group:SU(2)
M
N
- Nonabelian
- Normal subgroups
- Number of self-inverse conjugacy classes is equal to number of irreducible real characters
- Number of groups of order n is at most n to the power of (n log n)
- Number of groups function
O
- Omega subgroups of group of prime power order
- Order 4p
- Orbit
- Orbits
- Orbit-stabilizer theorem
- Order p
- Omega and agemo subgroups
- Order 88
- Order 152
- Order 344
- Order p^2q
- Order 22
- Orphaned pages
P
- Paper:Gaschutz54
- Proving join-closure
- PSL(2, 7)
- Pauli group
- Projective special unitary group:PSU(3,2)
- PSL(2,29)
- PSL(2,31)
- Paul Erdos
- Prufer group
- PID
Q
- Quaternion group:q8
- Quaternion group:Q8
- Quasidihedral group
- Quotient of cyclic group is cyclic
- Quadratic field extension
- Quartic field extension
- Quintic field extension
R
S
- Standard representation
- Subgroup structure of M16
- SmallGroup(36,2)
- SmallGroup(36,5)
- SmallGroup(36,8)
- SmallGroup(36,14)
- SmallGroup(36,1)
- SmallGroup(40,4)
- SmallGroup(36,12)
- Subrep
- Simplicity of A5
- Semisimple linear representation
- Semisimple representation
- Schurs lemma
- Semidirect products
- SmallGroup(70,2)
- SmallGroup(70,1)
- SmallGroup(70,4)
- SmallGroup(70,3)
- SmallGroup(42,3)
- Simple linear representation
- Simple representation
- Sign representation on symmetric group
- Standard representation of symmetric group
- Schur’s lemma
- Sum of irrep on conjugacy class is scalar multiple of identity matrix
- Sum of irreducible representation on conjugacy class is scalar multiple of identity
- Symmetric and exterior-squares of vector space
- Symmetric and alternating squares of vector space
- Symmetric and exterior squares of vector space
- Symmetric and alternating-squares of representation
- Symmetric and alternating-squares of a vector space
- SmallGroup(42,4)
- Sign representation
- Symmetric and exterior-squares of linear representation
- Symmetric and exterior-squares of representation
- Symmetric and exterior-squares
- SmallGroup(36,4)
- Second orthogonality relation
- Second orthogonality relation of characters
- Second orthogonality relation for characters
- Sporadic simple groups
- SmallGroup(60,7)
- SmallGroup(60,6)
- SmallGroup(64,262)
- Schur indicator
- SmallGroup(64,190)
- SmallGroup(256,56092)
- Sd16
- S3xZ3
- SmallGroup(144,183)
- SmallGroup(864,4661)
- SmallGroup(288,851)
- SmallGroup(96,189)
- SmallGroup(108,26)
- SmallGroup(56,2)
- SmallGroup(56,3)
- SmallGroup(56,4)
- SmallGroup(56,5)
- SmallGroup(56,6)
- SmallGroup(56,8)
- SmallGroup(56,9)
- SmallGroup(56,10)
- SmallGroup(56,12)
- SmallGroup(56,13)
- SmallGroup(56,1)
- SmallGroup(56,7)
- Special unitary group:SU(2)
- SmallGroup(120,39)
- SmallGroup(120,1)
- SmallGroup(120,2)
- SmallGroup(120,4)
- SmallGroup(120,6)
- SmallGroup(120,8)
- SmallGroup(120,9)
- SmallGroup(120,15)
- SmallGroup(120,16)
- SmallGroup(120,17)
- SmallGroup(120,18)
- SmallGroup(120,19)
- SmallGroup(120,20)
- SmallGroup(120,21)
- SmallGroup(120,22)
T
- Topological space
- Trivial representation
- Theorem of the primitive element
- Tensor representation of representations
- Trivial character
U
V
Z
5