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math.GR2013★ 13 cited
Random triangular groups at density 1/3
Sylwia Antoniuk, Tomasz Łuczak, Jacek Świcatkowski
Let Γ(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. Γ(n,p) is free and if p >= C log…
math.GR2013★ 5 cited
Collapse of random triangular groups: a closer look
Sylwia Antoniuk, Tomasz Łuczak, Jacek Świcatkowski
The random triangular group Γ(n,t) is a group given by a presentation P=<S|R>, where S is a set of n generators and R is a random set of t cyclically reduced words of length three.…