14 citations · 36 across the 10 of their papers we have counts for
4 papers · 1 filter
Freiheitssatz and phase transition for the density model of random groups
Tsung-Hsuan Tsai
Magnus' Freiheitssatz states that if a group is defined by a presentation with generators and a single relator containing the last generating letter, then the first lette…
A sharp threshold for collapse of the random triangular group
Sylwia Antoniuk, Ehud Friedgut, Tomasz Łuczak
The random triangular group is the group given by a random group presentation with generators in which every relator of length three is present independently with prob…
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…
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.…