Random triangular groups at density
Random triangular groups at density
Let \Gamma(n,p) denote the binomial model of a random triangular group. We show that there exist constants c, C > 0 such that if p <= c/n^2, then a.a.s. \Gamma(n,p) is free and if p >= C log n/n^2 then a.a.s. \Gamma(n,p) has Kazhdan's property (T). Furthermore, we show that …