Non-orderability of random triangular groups by using random 3CNF formulas

Abstract

We show that a random group $\Gamma$ in the triangular binomial model $\Gamma (n,p)$ is a.a.s. not left-orderable for $p\in (c{n}^{-2},n^{-3/2-\epsilon })$, where $c,\epsilon$ are any constants satisfying $\epsilon >0$, $c>(1/8){\log }_{4/3}2\approx 0.3012$. We also prove that if $p\ge (1+\epsilon )(\log n)n^{-2}$ for any fixed $\epsilon >0$, then a random $\Gamma \in \Gamma (n,p)$ has a.a.s. no non-trivial left-orderable quotients. We proceed by constructing 3CNF formulas, which encode necessary conditions for left-orderability and then proving their unsatisfiability a.a.s.

References in corpus (1)

• Freiheitssatz and phase transition for the density model of random groups