English

Free metabelian groups are permutation stable

Group Theory 2023-01-19 v1

Abstract

We prove that all finitely generated free metabelian groups are permutation stable. This partially answers to the question asked by Levit and Lubotzky whether all finitely generated metabelian groups are permutation stable. Our proof extends the range of application of Levit-Lubotzky's method, which is used to show permutation stability of permutational wreath products of finitely generated abelian groups, to non-split and non-permutational metabelian groups.

Keywords

Cite

@article{arxiv.2301.07586,
  title  = {Free metabelian groups are permutation stable},
  author = {Hiroki Ishikura},
  journal= {arXiv preprint arXiv:2301.07586},
  year   = {2023}
}
R2 v1 2026-06-28T08:14:35.539Z