A note on essentially indecomposable n-summable Abelian p-groups | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2018. № 51. DOI: 10.17223/19988621/51/2

A note on essentially indecomposable n-summable Abelian p-groups

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.

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Keywords

summable groups, essentially indecomposable groups, admissible Ulm functions, direct sums of countable groups, суммируемые группы, существенно неразложимые группы, допустимые функции Ульма, прямые суммы счетных групп

Authors

Name	Organization	E-mail
Danchev Peter V.	Plovdiv University "P. Hilendarski"	pvdanchev@yahoo.com

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References

Fuchs L. (1970, 1973) Infinite Abelian Groups. Vol. I , II. New York; London: Academic Press.

Danchev P.V. , Keef P.W. (2010) n-Summable valuated pn-socles and primary abelian groups. Commun. Algebra. 38(9). pp. 3137-3153.

Keef P.W. (2011) Realization theorems for valuated pn-socles. Rend. Sem. Mat. Univ. Padova. 126. pp.151-173.

Danchev P.V. (2012). Valuated pn-socles and Cx n-summable abelian p-groups. Pioneer J. Math. and Math. Sci. 6(2). pp. 233-249.

Danchev P.V. (2013) A note on pM+n+2-projective efi n-summable abelian p-groups. Adv. Appl. Math. Sci. 12(3). pp. 151-155.

Danchev P.V., Keef P.W. (2009) Generalized Wallace theorems. Math. Scand. 104(1). pp. 33-50.