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Group homomorphism
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Short description
: Mathematical function between groups that preserves multiplication structure
Depiction of a group homomorphism (
h
) from
G
(left) to
H
(right). The oval inside
H
is the
image
of
h
.
N
is the
kernel
of
h
and
aN
is a
coset
of
N
.
Algebraic structure
→
Group theory
Group theory
Basic notions
Subgroup
Normal subgroup
Quotient group
(Semi-)
direct product
Group homomorphisms
kernel
image
direct sum
wreath product
simple
finite
infinite
continuous
multiplicative
additive
cyclic
abelian
dihedral
nilpotent
solvable
List of group theory topics
Finite groups
Classification of finite simple groups
cyclic
alternating
Lie type
sporadic
Lagrange's theorem
Sylow theorems
Hall's theorem
p-group
Elementary abelian group
Frobenius group
Schur multiplier
Symmetric group
S
n
Klein four-group
V
Dihedral group
D
n
Quaternion group
Q
Dicyclic group
Dic
n
Discrete groups
Lattices
Integers
(
Z
)
Free group
Modular groups
PSL(2,
Z
)
SL(2,
Z
)
Arithmetic group
Lattice
Hyperbolic group
Topological
and
Lie groups
Solenoid
Circle
General linear
GL(
n
)
Special linear
SL(
n
)
Orthogonal
O(
n
)
Euclidean
E(
n
)
Special orthogonal
SO(
n
)
Unitary
U(
n
)
