On lattice coverings of Nil space by congruent geodesic balls (Q1949859)

The paper under review works with a projective model of \textbf{Nil} space, see [\textit{E.\ Molnár}, Beiträge Algebra Geom.\ 38, No.\ 2, 261--288 (1997; Zbl 0889.51021)]. The author explains discrete translation groups and defines \textbf{Nil} point lattices as orbits of single points under these groups. A family of geodesic balls of the same radius centered at the points of a lattice is called a lattice-like geodesic ball covering if the union of its balls covers the whole space. The density of a lattice covering is introduced and upper and lower estimates of the smallest possible density of a lattice covering are established. The author formulates a conjecture concerning structure and density of the least dense lattice covering.