Up to isomorphism, how many additive abelian groups G of order 16 have the property that x + x + x + x = 0 for each x in G ?

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∻Solution by Steps∻ ‖ step 1 ⋮ Determine the number of abelian groups of order 16 using the function FiniteAbelianGroupCount. ‖ ‖ step 2 ⋮ Apply the function: FiniteAbelianGroupCount[16]. ‖ ‖ step 3 ⋮ The output of the function is 5, which means there are 5 non-isomorphic abelian groups of order 16. ‖ ∻Answer∻ ⚹ There are 5 non-isomorphic additive abelian groups G of order 16 such that x + x + x + x = 0 for each x in G. ⚹ ∻Key Concept∻ ⚹Classification of finite abelian groups⚹ ∻Explanation∻ ⚹The number of non-isomorphic abelian groups of a given order can be determined using the function FiniteAbelianGroupCount, which is based on the classification theorem for finite abelian groups. This theorem states that every finite abelian group is a direct sum of cyclic groups of prime power order. For order 16, which is $2^4$, there are 5 such groups.⚹◊What is the general formula for calculating the number of additive abelian groups of order $n$ satisfying the property $x + x + x + x = 0$ for each $x \in G$?⍭ Generate me a similar question◊

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