Magnus’ Freiheitssatz [20] states that if a group is defined by presentation with m generators and single cyclically reduced relator, this relator contains the last generating letter, then first $$m-1$$ letters freely generate free subgroup. We study an analogue of theorem in Gromov density model random groups [14], showing phase transition phenomenon at $$d_r = \min \{\frac{1}{2}, 1-\log _{2m-...

The Cavicchioli-Hegenbarth-Repovš generalized Fibonacci groups are defined by the presentationsGn(m, k) = 〈 x1, . . . , xn | xixi+m = xi+k (1 ≤ i ≤ n) 〉. These cyclically presented groups generalize Conway’s Fibonacci groups and the Sieradski groups. Building on a theorem of Bardakov and Vesnin we classify the aspherical presentations Gn(m, k). We determine when Gn(m, k) has infinite abelianiza...

We exhibit a family of infinite, finitely-presented, nilpotent-byabelian groups. Each member of this family is a solvable S-arithmetic group that is related to Baumslag-Solitar groups, and everyone of these groups has a quasi-isometry group that is virtually a product of a solvable real Lie group and a solvable p-adic Lie group. In addition, we propose a candidate for a polycyclic group whose q...

The article explores the issues of supplier evaluation and selection in organization's procurement management, which is particularly important context dynamics logistics networks under influence modern market trends. suitable suppliers affects performance system and, consequently, results company's activities. As a result study algorithm technique were developed enable to increase objectivity c...