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 
. This decomposition is unique, and the number of direct summands
is equal to the group rank of the Abelian
group.
Kronecker Basis Theorem
See also
Kronecker Decomposition TheoremThis entry contributed by Margherita Barile
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References
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 TheoremCite this as:
Barile, Margherita. "Kronecker Basis Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/KroneckerBasisTheorem.html