On The Intersection of Semi-Pure Subgroups of Abelian Group

H. M. A.  Abdullal; Luma J.  Barghooth

doi:10.24996/ijs.2020.SI.1.26

Authors

H. M. A. Abdullal Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq
Luma J. Barghooth Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.SI.1.26

Keywords:

Abelian group, Subgroups, Semi-pure subgroups, Minimal pure subgroup

Abstract

The following question was raised by L.Fuchs: "what are the subgroups of an abelian group G that can be represented as intersections of pure subgroups of G ? . Fuchs also added that â€œOne of my main aims is to give the answers to the above question". In this paper, we shall define new subgroups which are a family of the pure subgroups. Then we shall answer problem 2 of L.Fuchs by these semi-pure subgroups which can be represented as the intersections of pure subgroups.