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
Received: 28 March 2017 / Revised: 20 April 2017 / Accepted: 4 May 2017 / Published: 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
; (ii) if
, then there exists a subgroup
(the bounding number) such that
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.
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).
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MDPI and ACS Style
Paolini, G.; Shelah, S. No Uncountable Polish Group Can be a Right-Angled Artin Group. Axioms 2017, 6, 13.
Paolini G, Shelah S. No Uncountable Polish Group Can be a Right-Angled Artin Group. Axioms. 2017; 6(2):13.
Paolini, Gianluca; Shelah, Saharon. 2017. "No Uncountable Polish Group Can be a Right-Angled Artin Group." Axioms 6, no. 2: 13.
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