Abelian group theory

thumb|upright=1.25|The integers arranged on a number line

group whose group operation is commutative

mathematical group that can be generated as the set of powers of a single element

A commutative group where every element is the sum of elements from one finite subset

mathematical term

commutative associative binary operation on subsets of an Abelian group (such as Euclidean space)

commutative group whose elements are unique integer combinations of basis elements

abelian group in which every element can, in some sense, be divided by positive integers

subgroup of A consisting of all elements that have finite order

elements of a module space sent to 0 by regular elements of a ring

commutative group in which all nonzero elements have the same order

category in mathematics

the cardinality of a maximal linearly independent subset

topological group whose group is abelian