2017/01/08 by Paolini, Gianluca, Shelah, Saharon
#03C60 #03E15 #20B27 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1701.03021
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 < ω, then lg(x) ≤ lg(xk); (ii) if lg(y) < k < ω and xk = 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 [3] and [5], where this is proved for free and free Abelian uncountable groups.