MODNET

Research Training Network in Model Theory

Publications > Preprint server > Preprint Number 1133
Preprint Number 1133
1133. Albert Garreta, Alexei Miasnikov, Denis Ovchinnikov Random nilpotent groups, polycyclic presentations, and Diophantine
problems E-mail: Submission date: 8 December 2016 Abstract: We introduce a model of random f.g., torsion-free, 2-step nilpotent groups
(in short, τ_2-groups). To do so, we show that these are precisely the
groups that admit a presentation of the form ⟨ A, C
| [a_i, a_j]= ∏_t c_t^{λ_{t,i,j}}}, (i< j), [A,C]=[C,C]=1 ⟩, where A= {a_1, ... ,
a_n }, and C={ c_1, \dots, c_m }. Hence, one may select a random
τ_2-group G by fixing A and C, and then randomly choosing exponents
λ_{t,i,j} with |λ_{t,i,j}| ≤ l, for some l. Mathematics Subject Classification: Keywords and phrases: |

Last updated: December 12 2016 12:56 | Please send your corrections to: |