Translator Disclaimer
May 2007 Purifiability in pure subgroups
Takashi OKUYAMA
Hokkaido Math. J. 36(2): 365-381 (May 2007). DOI: 10.14492/hokmj/1277472809

Abstract

Let $G$ be an abelian group. A subgroup $A$ of $G$ is said to be {\it purifiable} in $G$ if, among the pure subgroups of $G$ containing $A$, there exists a minimal one. Suppose that $A$ is purifiable in $G$ and $H$ is a pure subgroup of $G$ containing $A$. Then $A$ need not be purifiable in $H$. In this note, we ask for conditions that guarantee that $A$ is purifiable in the intermediate group $H$. First, we prove that if $A$ is a torsion--free purifiable subgroup of a group $G$ and $H$ is a direct summand of $G$ containing $A$, then $A$ is purifiable in $H$. Next, we characterize the pure subgroups $K$ of a group $G$ with the property that a torsion--free finite rank subgroup $A$ of $K$ is purifiable in $K$ if $A$ is purifiable in $G$.

Citation

Download Citation

Takashi OKUYAMA. "Purifiability in pure subgroups." Hokkaido Math. J. 36 (2) 365 - 381, May 2007. https://doi.org/10.14492/hokmj/1277472809

Information

Published: May 2007
First available in Project Euclid: 25 June 2010

zbMATH: 1142.20031
MathSciNet: MR2347431
Digital Object Identifier: 10.14492/hokmj/1277472809

Subjects:
Primary: 20K21
Secondary: 20K27

Rights: Copyright © 2007 Hokkaido University, Department of Mathematics

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.36 • No. 2 • May 2007
Back to Top