Loading...
Please wait, while we are loading the content...
Similar Documents
Random triangular groups at density
| Content Provider | Scilit |
|---|---|
| Author | Antoniuk, Sylwia Łuczak, Tomasz Świa̧tkowski, Jacek |
| Copyright Year | 2014 |
| Description | Journal: Compositio Mathematica Let ${\rm\Gamma}(n,p)$ denote the binomial model of a random triangular group. We show that there exist constants $c,C>0$ such that if $p\leqslant c/n^{2}$, then asymptotically almost surely (a.a.s.) ${\rm\Gamma}(n,p)$ is free, and if $p\geqslant C\log n/n^{2}$, then a.a.s. ${\rm\Gamma}(n,p)$ has Kazhdan’s property (T). Furthermore, we show that there exist constants $C^{\prime },c^{\prime }>0$ such that if $C^{\prime }/n^{2}\leqslant p\leqslant c^{\prime }\log n/n^{2}$, then a.a.s. ${\rm\Gamma}(n,p)$ is neither free nor has Kazhdan’s property (T). |
| Ending Page | 178 |
| Starting Page | 167 |
| ISSN | 00221295 |
| e-ISSN | 15705846 |
| DOI | 10.1112/s0010437x14007805 |
| Journal | Compositio Mathematica |
| Issue Number | 1 |
| Volume Number | 151 |
| Language | English |
| Publisher | Wiley-Blackwell |
| Publisher Date | 2015-01-01 |
| Access Restriction | Open |
| Subject Keyword | Journal: Compositio Mathematica Mathematical Physics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Algebra and Number Theory |
