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ON GROUPS WHICH CONTAIN NO HNN-EXTENSIONS

DEREK J. S. ROBINSON

Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

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ALESSIO RUSSO

Dipartimento di Matematica, Seconda Università di Napoli, Via Vivaldi 43, 81100 Caserta, Italy

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GIOVANNI VINCENZI

Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte Don Melillo 4, 84084 Fisciano (Salerno), Italy

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https://doi.org/10.1142/S0218196707004311Cited by:9 (Source: Crossref)

Abstract

A group is called HNN-free if it has no subgroups that are nontrivial HNN-extensions. We prove that finitely generated HNN-free implies virtually polycyclic for a large class of groups. We also consider finitely generated groups with no free subsemigroups of rank 2 and show that in many situations such groups are virtually nilpotent. Finally, as an application of our results, we determine the structure of locally graded groups in which every subgroup is pronormal, thus generalizing a theorem of Kuzennyi and Subbotin.

Keywords:

AMSC: Primary 20E06

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