Kronecker Basis Theorem

A generalization of the Kronecker decomposition theorem which states that every finitely generated Abelian group is isomorphic to the group direct sum of a finite number of groups, each of which is either cyclic of prime power order or isomorphic to Z. This decomposition is unique, and the number of direct summands is equal to the group rank of the Abelian group.

See also

Kronecker Decomposition Theorem

This entry contributed by Margherita Barile

Explore with Wolfram|Alpha


Kargapolov, M. I. and Merzljako, Ju. I. Fundamentals of the Theory of Groups. New York: Springer-Verlag, p. 55, 1979.Schenkman, E. Group Theory. Princeton, NJ: Van Nostrand, p. 48, 1965.

Referenced on Wolfram|Alpha

Kronecker Basis Theorem

Cite this as:

Barile, Margherita. "Kronecker Basis Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

Subject classifications