Geometric and Asymptotic Group Theory with Applications (GAGTA 14) Workshop (07 - 11 June)
Olga Kharlampovich CUNY Hunter College and Graduate Center
First-order formulas in random groups
We will use Gromov's density model of randomness.
A random group at density d satisfies some property (of groups) P if the probability of
occurrence of P tends to 1 as the length of relations goes to infinity. J. Knight conjectured
that a first-order sentence is true in a nonabelian free group if and only if it almost surely
true in a "random group". We will show that this is true for universal sentences at
density d<1/16. We will also show that a random group at density d<1/2 is not a limit group
(for a few relator model this was shown by Ho). These are joint results with R. Sklinos.