Rank of an abelian group information

mathematics, the rank, Prüfer rank, or torsion-free rank of an abelian group A is the cardinality of a maximal linearly independent subset. The rank of A determines...

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, 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...

quotient group) of a group G then rank(H) ≤ rank(G). If G is a finite non-abelian simple group (e.g. G = An, the alternating group, for n > 4) then rank(G)...

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

Rank (set theory) Rank (type theory) Rank of an abelian group, the cardinality of a maximal linearly independent subset Rank of a free module Rank of...

mathematics, the Grothendieck group, or group of differences, of a commutative monoid M is a certain abelian group. This abelian group is constructed from M in...

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...

integers are also a free abelian group, although all free groups of rank ≥ 2 {\displaystyle \geq 2} are non-abelian. A free group on a two-element set S...

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...

of involutions resemble those of groups of Lie type over fields of characteristic 2, and the width is roughly the maximal rank of an abelian group of...

a finitely generated abelian group is the direct sum of a free abelian group of finite rank and a finite abelian group, each of which are unique up to...

automorphism group Quotient group Examples of groups Abelian group Cyclic group Rank of an abelian group Dicyclic group Dihedral group Divisible group Finitely...

arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the studies of Pierre...

is simply a finitely generated abelian group. The left R-module M is finitely generated if there exist a1, a2, ..., an in M such that for any x in M,...

In the theory of abelian groups, the torsion subgroup AT of an abelian group A is the subgroup of A consisting of all elements that have finite order...

work for groups with elementary abelian subgroups of rank at least 3.) A group is said to be of component type if for some centralizer C of an involution...

group Abelian group Torsion subgroup Free abelian group Finitely generated abelian group Rank of an abelian group Cyclic group Locally cyclic group Solvable...

and the algebra of left-invariant differential operators. An S-group scheme G is commutative if the group G(T) is an abelian group for all S-schemes...

and hence not an abelian variety. The quotient Pic(V)/Pic0(V) is a finitely-generated abelian group denoted NS(V), the Néron–Severi group of V. In other...