Result: Some torsion-free solvable groups with few subquotients

Title:
Some torsion-free solvable groups with few subquotients
Authors:
Le Boudec, Adrien, Matte Bon, Nicolás
Contributors:
Matte Bon, Nicolás, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Algèbre, géométrie, logique (AGL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)
Source:
Mathematical Proceedings of the Cambridge Philosophical Society. 176:279-286
Publication Status:
Preprint
Publisher Information:
Cambridge University Press (CUP), 2023.
Publication Year:
2023
Subject Terms:
0103 physical sciences, FOS: Mathematics, Group Theory (math.GR), 0101 mathematics, Mathematics - Group Theory, 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]
Document Type:
Academic journal Article
File Description:
application/pdf
Language:
English
ISSN:
1469-8064
0305-0041
DOI:
10.1017/s0305004123000506
DOI:
10.48550/arxiv.2206.06689
Access URL:
http://arxiv.org/abs/2206.06689
https://hal.science/hal-03810038v2
https://doi.org/10.1017/s0305004123000506
https://hal.science/hal-03810038v2/document
Rights:
Cambridge Core User Agreement
CC BY
Accession Number:
edsair.doi.dedup.....eb2b8d1417b9ec8b4426de1415f01c6c
Database:
OpenAIRE

Further Information

We construct finitely generated torsion-free solvable groups G that have infinite rank, but such that all finitely generated torsion-free metabelian subquotients of G are virtually abelian. In particular all finitely generated metabelian subgroups of G are virtually abelian. The existence of such groups shows that there is no “torsion-free version” of P. Kropholler’s theorem, which characterises solvable groups of infinite rank via their metabelian subquotients.