On \(m\)-\(\omega_1\)-\(p^{\omega+n}\)-projective Abelian \(p\)-groups.
type: Item
instance of: scholarly article
title: On \(m\)-\(\omega_1\)-\(p^{\omega+n}\)-projective Abelian \(p\)-groups.
zbMATH Open document ID: 1312.20049
published in: Demonstratio Mathematica
publication date: 2015-01-26T00:00:00Z
review text: This paper is part of a long sequence of the author's in which he generalizes previously studied properties of infinite abelian \(p\)-groups. In this case, his main definition is that \(G\) is \(m\)-\(\omega_1\)-\(p^{\omega+n}\)-projective if \(G\) has a \(p^m\)-bounded subgroup \(A\) such that \(G/A\) is strongly \(\omega_1\)-\(p^{\omega+n}\)-projective, the latter property being one defined in the previous paper in the sequence. He defines a variety of further generalizations by restricting the subgroup \(A\) to lie in various classes of groups. The author then studies the relations among these properties and the inheritance of the properties under the operations \(G\to p^\lambda G\) and \(G\to G/p^\lambda G\) for various ordinals \(\lambda\). The paper concludes with problems suggesting that further generalizations are in store.
reviewed by: Phillip Schultz
Mathematics Subject Classification ID: 20K10
Mathematics Subject Classification ID: 20K27
Mathematics Subject Classification ID: 20K40
zbMATH DE Number: 6390747
zbMATH Keywords: projective Abelian \(p\)-groups
zbMATH Keywords: bounded subgroups
zbMATH Keywords: \(p^{\omega+n}\)-projective groups
zbMATH Keywords: strongly \(\omega_1\)-\(p^{\omega+n}\)-projective groups
zbMATH Keywords: countable subgroups
zbMATH Keywords: nice subgroups
zbMATH Keywords: Ulm subgroups
zbMATH Keywords: Ulm factors
author: Peter Danchev
MaRDI profile type: Publication
full work available at URL: dema-2014-0065
OpenAlex ID: W2067045854
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DOI: 10.2478/DEMA-2014-0065
description: scientific article; zbMATH DE number 6390747