Ascending HNN extensions of residually finite groups can be non-Hopfian and can have very few finite quotients

DOI10.1016/S0022-4049(01)00003-2zbMath0995.20013OpenAlexW2111253327WikidataQ127172359 ScholiaQ127172359MaRDI QIDQ5956877

Mark V. Sapir, Daniel T. Wise

Publication date: 21 October 2002

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(01)00003-2

zbMATH Keywords

finitely generated residually finite groupsascending HNN extensions

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Residual properties and generalizations; residually finite groups (20E26)

Related Items (7)

On the isolated points in the space of groups. ⋮ A family of two-generator non-Hopfian groups ⋮ Groups with the same cohomology as their profinite completions. ⋮ Amenable groups without finitely presented amenable covers ⋮ Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms ⋮ Ascending HNN extensions of polycyclic groups are residually finite. ⋮ An uncountable family of finitely generated residually finite groups

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