The $OP$ subgroup of a torsion-free LCA group

Aliakbar Alijani

doi:10.5644/SJM.22.01.03

The $OP$ subgroup of a torsion-free LCA group

Authors

Aliakbar Alijani Department of Basic Sciences, Faculty of Basic and General Studies, Technical and Vocational University(TVU), Tehran, Iran

DOI:

https://doi.org/10.5644/SJM.22.01.03

Keywords:

OP subgroup, Pure subgroup, Extension

Abstract

Let $G$ be a locally compact abelian (LCA) group. We denote by $G_{op}$, the intersection of all open pure subgroups of $G$, which we call the $OP$ subgroup of $G$. In this paper, we prove that the $OP$ subgroup of a non-discrete, torsion-free LCA group $G$ is a non-zero pure subgroup of $G$.

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References

D. L. Armacost, On pure subgroups of LCA groups, Proc. Amer. Math. Soc., 45 (1974), 414–418.

L. Fuchs, Infinite Abelian Groups, Vol. I, Academic Press, New York, 1970.

E. Hewitt and K. Ross, Abstract Harmonic Analysis, Vol. I, Second Edition, Springer-Verlag, Berlin, 1979.

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Published

27.07.2026

How to Cite

Alijani, A. (2026). The $OP$ subgroup of a torsion-free LCA group. Sarajevo Journal of Mathematics, 22(01), 41–43. https://doi.org/10.5644/SJM.22.01.03