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 25 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 27 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.
On Groups which contain no HNN-extension
VINCENZI, Giovanni
2007-01-01
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 25 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 27 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.File in questo prodotto:
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