Geodesic
On a Theorem of Cutler
Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 225-227

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In [1] Cutler proved the following theorem.Theorem. If G and K are abelian groups such that nG ≅ nK for some positive integer n, then there are abelian groups U and V such that U ⊕ G ≅ V ⊕ K and nU = 0 = nV.Cutler's proof is long and fairly involved. Walker [3] obtains the theorem rather elegantly as a corollary of his results on n-extensions. We give here a proof that is extremely simple both in conception and execution. Our proof relies on the notion of p-basic subgroups introduced by Fuchs in [2]. Therefore we shall first recall certain pertinent facts from [2]. 
Megibben, Charles K. On a Theorem of Cutler. Canadian mathematical bulletin, Tome 12 (1969) no. 2, pp. 225-227. doi: 10.4153/CMB-1969-027-x
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     title = {On a {Theorem} of {Cutler}},
     journal = {Canadian mathematical bulletin},
     pages = {225--227},
     year = {1969},
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     number = {2},
     doi = {10.4153/CMB-1969-027-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-027-x/}
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