Classify All Abelian Groups of Order 1000, Up to Isomorphism

Let G be an Abelian group of order 1000 = 2^3*5^3. Up to isomorphism, can we classify the possibilities for G? In other words, what are its possible isomorphism classes? By the Fundamental Theorem of Finite Abelian groups, G is either cyclic or isomorphic to a direct product of cyclic groups of prime power order. The number of possible isomorphism classes is related to the integer partitions of the powers of the primes in the prime factorization of the order of G.

#GroupTheory #AbstractAlgebra #AbelianGroup #isomorphism

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