Non-hopfian relatively free groups

2003/12/29 by S. V. Ivanov, Ivanov, S. V., A. M. Storozhev +1
Mathematics · #20E10 #20F05 #20F06 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E10 #msc:20F05 #msc:20F06

paper · pdf · doi:10.48550/arxiv.math/0312491

17 pages

arxiv created 2003/12/29 · openalex publication_date 2003/12/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

To solve problems of Gilbert Baumslag and Hanna Neumann, posed in the 1960's, we construct a nontrivial variety of groups all of whose noncyclic free groups are non-hopfian.

Related

• A non-Hopfian relatively hyperbolic group with respect to a Hopfian subgroup
• The construction principle and non homogeneity of uncountable relatively free groups
• Non-∀-homogeneity in free groups
• Embeddings of relatively free groups into finitely presented groups
• Uniform non--amenability of free Burnside groups