In 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 ...
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In group theory, an abelian group is a group with operation that is commutative. Because of that, an abelian group is sometimes called a 'commutative group'.
Lattice theory studies free abelian subgroups of real vector spaces. In algebraic topology, free abelian groups are used to define chain groups, and in ...
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... abelian 2-group) is sometimes called a Boolean group. ... In general, a (possibly infinite) elementary abelian p-group is a direct sum of cyclic groups of order p ...
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So, finitely generated abelian groups can be thought of as a generalization of cyclic groups. Every finite abelian group is finitely generated. The finitely ...
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For finitely generated abelian groups, rank is a strong invariant and every such group is determined up to isomorphism by its rank and torsion subgroup. Torsion ...
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, a group in which the binary operation is commutative. Category of abelian groups (Ab), has abelian groups as objects and group homomorphisms as morphisms.
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In several mathematical areas, including harmonic analysis, topology, and number theory, locally compact abelian groups are abelian groups which have a ...
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