abelian group
group whose group operation is commutative
ideal
additive subgroup of a ring closed under multiplcation by arbitrary ring element
central subgroup
subgroup lying inside the center of the group
free abelian group
commutative group whose elements are unique integer combinations of basis elements
abelian variety
projective abelian algebraic group
Brauer group
abelian group related to division algebras
finitely generated abelian group
A commutative group where every element is the sum of elements from one finite subset
cyclic group
mathematical group that can be generated as the set of powers of a single element
Witt group
algebra term
locally compact abelian group
topological group structure arising in Fourier analysis
module
generalization of vector space, with scalars in a ring instead of a field
torsion-free abelian group
group in which the group operation is commutative and the identity element is the only element with finite order
maximal torus
maximal compact connected Abelian Lie subgroup
character group
group of group homomorphisms from a group into the multiplication group of nonzero elements of a field
divisible group
abelian group in which every element can, in some sense, be divided by positive integers
algebraic torus
commutative affine algebraic group
Cartan subgroup
maximal connected Abelian subgroup
torsion abelian group
abelian group in which every element has finite order
divisor class group
group of Weil divisors
elementary abelian group
commutative group in which all nonzero elements have the same order