Work

Free metabelian groups are permutation stable

Year: 2024

Type: article

Abstract: We prove that all finitely generated free metabelian groups are permutation stable by verifying that all invariant random subgroups of them are co-sofic. 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 and 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.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/833

Author: Hiroki Ishikura

Institution: The University of Tokyo

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Award: 軌道同値関係から見る局所コンパクト群のsofic近似列