# Sh:1112

• Paolini, G., & Shelah, S. (2017). No uncountable Polish group can be a right-angled Artin group. Axioms Topical Collection “Topological Groups", 6(2), 4. arXiv: 1701.03021
• Abstract:
We prove that no uncountable Polish group can admit a system of generators whose associated length function satisfies the following conditions: (i) if 0 < k < \omega, then lg(x) \leq lg(x^k); (ii) if lg(y) < k < \omega and x^k = y, then x = e. In particular, the automorphism group of a countable structure cannot be an uncountable right-angled Artin group. This generalizes results from [Sh:744] and "Polish Group Topologies" by S. Solecki, where this is proved for free and free abelian uncountable groups.
• published version (4p)
Bib entry
@article{Sh:1112,
author = {Paolini, Gianluca and Shelah, Saharon},
title = {{No uncountable Polish group can be a right-angled Artin group}},
journal = {Axioms Topical Collection Topological Groups"},
volume = {6(2)},
year = {2017},
pages = {4},
note = {\href{https://arxiv.org/abs/1701.03021}{arXiv: 1701.03021}},
arxiv_number = {1701.03021}
}