Torsion-free Abelian groups with finite groups of automorphisms
type: Item
instance of: scholarly article
title: Torsion-free Abelian groups with finite groups of automorphisms
zbMATH Open document ID: 0605.20053
DOI: 10.1007/BF01156671
author: V. A. Nikiforov
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: The main result of this paper is theorem 5: If a finite group \(\Gamma\) is the automorphism group of some abelian group, then for any cardinal \(\mathfrak M\) less than the first nonmeasurable cardinal there are \(2^{\mathfrak M}\) nonisomorphic abelian groups of cardinality \(\mathfrak M\) with automorphism group \(\Gamma\).
reviewed by: A. M. Sebel'din
Mathematics Subject Classification ID: 20K30
Mathematics Subject Classification ID: 20K20
Mathematics Subject Classification ID: 20F29
zbMATH DE Number: 3977277
zbMATH Keywords: finite group
zbMATH Keywords: automorphism group
zbMATH Keywords: abelian groups
MaRDI profile type: Publication
cites work: Torsion-free groups having finite automorphism groups. I
cites work: Finite Automorphism Groups of Torsion-Free Groups
cites work: Every Cotorsion-Free Ring is an Endomorphism Ring
cites work: Die Konstruktion von Gruppen mit vorgeschriebenen Automorphismengruppen.
cites work: Finite groups of exponent 4 as automorphism groups. II
cites work: Groups of exponent 4 as automorphism groups
description: scientific article; zbMATH DE number 3977277