Misbehaved direct products
type: Item
instance of: scholarly article
title: Misbehaved direct products
zbMATH Open document ID: 1020.20022
DOI: 10.1016/S0723-0869(02)80013-5
author: Ron Hirshon
published in: Expositiones Mathematicae
publication date: 2003-09-23T00:00:00Z
review text: The author presents with leisurely discussion 3 deceptively difficult open problems concerning direct products of groups. The first is whether the direct product of a Hopfian group and the infinite cyclic group is necessarily Hopfian. The second is whether a finitely presented group can be a proper direct factor of itself. The third (labelled ``for quick fame'') is more technical and related to the Poincaré conjecture.
reviewed by: G. E. Wall
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20E22
zbMATH DE Number: 1870161
zbMATH Keywords: direct products of groups
zbMATH Keywords: Hopfian groups
zbMATH Keywords: finitely presented groups
zbMATH Keywords: Poincaré conjecture
zbMATH Keywords: free products
MaRDI profile type: Publication
cites work: Groups without proper isomorphic quotient groups
cites work: On abelian hopfian groups. I
cites work: Some two-generator one-relator non-Hopfian groups
cites work: Some Odd Finitely Presented Groups
cites work: On the question of the Hopficity of the direct product of a Hopfian with an infinite cyclic group
cites work: Three examples on hopficity in torsion-free abelian groups
cites work: Q4157686
cites work: Free products of Hopf groups
cites work: A Finitely Related Group with An Isomorphic Proper Factor Group
cites work: Some Theorems on Hopficity
cites work: On Hopfian groups
cites work: The center and the commutator subgroup in hopfian groups
cites work: A conjecture on Hopficity and related results
cites work: The direct product of a hopfian group with a group with cyclic center
cites work: The direct product of a Hopfian group with a p-group
cites work: The cancellation of an infinite cyclic group in direct products
cites work: Cancellation and Hopficity in direct products
cites work: The Equivalence of × t C ≈× t D and J × C ≈J × D
cites work: Finitely generated groups L with \(L\approx L\times M\), \(M\neq 1\), M finitely presented
cites work: Some properties of groups which allow homomorphisms onto their direct square
cites work: Heegaard Splittings and Splitting Homomorphisms
cites work: Direct products and the Hopf property
cites work: Q4145882
cites work: Non-Hopfian Groups
cites work: Groups with a quotient that contains the original group as a direct factor
cites work: Embeddings into hopfian groups
cites work: A Two-Generator Group Isomorphic to a Proper Factor Group
cites work: The Hopf property of free products
cites work: Hanna Neumann
cites work: Q5331572
cites work: On the recursiveness of sets of presentations of 3-manifold groups
description: scientific article; zbMATH DE number 1870161