Geodesic
A note on essentially indecomposable $n$-summable Abelian $p$-groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 51 (2018), pp. 15-18

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For each natural $n$ we prove that there exists an unbounded $n$-summable abelian $p$-group which is essentially indecomposable. This example parallels a well-known result of this kind established for separable abelian $p$-groups.
Keywords: summable groups, essentially indecomposable groups, admissible Ulm functions, direct sums of countable groups. 
@article{VTGU_2018_51_a1,
     author = {P. V. Danchev},
     title = {A note on essentially indecomposable $n$-summable {Abelian} $p$-groups},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {15--18},
     publisher = {mathdoc},
     number = {51},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2018_51_a1/}
}
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P. V. Danchev. A note on essentially indecomposable $n$-summable Abelian $p$-groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 51 (2018), pp. 15-18. http://geodesic.mathdoc.fr/item/VTGU_2018_51_a1/