Next Article in Journal
Tsallis Entropy and Generalized Shannon Additivity
Next Article in Special Issue
Categorically Closed Topological Groups
Previous Article in Journal
Toward Measuring Network Aesthetics Based on Symmetry
Previous Article in Special Issue
An Overview of Topological Groups: Yesterday, Today, Tomorrow
Open AccessArticle

No Uncountable Polish Group Can be a Right-Angled Artin Group

Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel
Department of Mathematics, The State University of New Jersey, Hill Center-Busch Campus, Rutgers, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA
Author to whom correspondence should be addressed.
Academic Editor: Sidney A. Morris
Axioms 2017, 6(2), 13;
Received: 28 March 2017 / Revised: 20 April 2017 / Accepted: 4 May 2017 / Published: 11 May 2017
(This article belongs to the Collection Topological Groups)
PDF [220 KB, uploaded 11 May 2017]


We prove that if G is a Polish group and A a group admitting a system of generators whose associated length function satisfies: (i) if 0 < k < ω , then l g ( x ) l g ( x k ) ; (ii) if l g ( y ) < k < ω and x k = y , then x = e , then there exists a subgroup G * of G of size b (the bounding number) such that G * is not embeddable in A. In particular, we prove that the automorphism group of a countable structure cannot be an uncountable right-angled Artin group. This generalizes analogous results for free and free abelian uncountable groups. View Full-Text
Keywords: descriptive set theory; polish group topologies; right-angled Artin groups descriptive set theory; polish group topologies; right-angled Artin groups
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Printed Edition Available!
A printed edition of this Special Issue is available here.

Share & Cite This Article

MDPI and ACS Style

Paolini, G.; Shelah, S. No Uncountable Polish Group Can be a Right-Angled Artin Group. Axioms 2017, 6, 13.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top