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...

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...

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...

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...

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...

is an elementary abelian group and its automorphism group is a general linear group, so very well understood. The map from the automorphism group of G...

rank has a different meaning in the context of elementary abelian groups. A subset {aα} of an abelian group A is linearly independent (over Z) if the only...

abelian group, if m denotes the maximum of all the orders of the group's elements, then every element's order divides m. Suppose G is a finite group of...

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...

algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is commutative...