mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does...

In abstract algebra, an abelian group ( G , + ) {\displaystyle (G,+)} is called finitely generated if there exist finitely many elements x 1 , … , x s...

In mathematics, a free abelian group is an abelian group with a basis. Being an abelian group means that it is a set with an addition operation that is...

mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists at...

an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines the size of the largest free abelian group contained...

algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by...

In mathematics, specifically in group theory, an elementary abelian group is an abelian group in which all elements other than the identity have the same...

notion is a free abelian group; both notions are particular instances of a free object from universal algebra. As such, free groups are defined by their...

specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently...

In mathematics, the Klein four-group is an abelian group with four elements, in which each element is self-inverse (composing it with itself produces...