The square model for random groups

• Autorzy: Tomasz Odrzygóźdź
• Języki publikacji: EN

Abstrakty

EN

We introduce a new random group model called the square model: we quotient a free group on n generators by a random set of relations, each of which is a reduced word of length 4. We prove that, just as in the Gromov model, for densities > 1/2 a random group in the square model is trivial with overwhelming probability and for densities < 1/2 a random group is hyperbolic with overwhelming probability. Moreover, we show that for densities d < 1/3 a random group in the square model does not have Property (T). Inspired by the results for the triangular model, we prove that for densities < 1/4 in the square model, a random group is free with overwhelming probability. We also introduce abstract diagrams with fixed edges and prove a generalization of the isoperimetric inequality.

Kategorie tematyczne

• 20F65: Geometric group theory
• 20F67: Hyperbolic groups and nonpositively curved groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 142
• Numer: 2
• Strony: 227-254

Daty

wydano

2016

Twórcy

autor

Tomasz Odrzygóźdź

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-656 Warszawa, Poland

Identyfikatory

DOI

10.4064/cm142-2-5