Some aspects of separability

Conjugacy Separability of Some One-Relator Groups

Conjugacy separability of any group of the class of one-relator groups given by the presentation a, b; a m , b n 1m, n > 1 is proven. The proof made used of theoretical combinatorial group methods, namely the structure of amalgamated free products and some properties of the subgroups and quotients of any group of the class of one-relator groups given above.

Some Lower Bounds on Geometric Separability Problems

We obtain lower bounds in the algebraic computation tree model for deciding the separability of two disjoint point sets. In particular, we show Ω(n log n) time lower bounds for separability by means of strips, wedges, wedges with apices on a given line, fixed-slopes double wedges, and triangles, which match the complexity of the existing algorithms, and therefore prove their optimality.

Some Separability Problems in the Plane

Some combinatorial aspects of finite Hamiltonian groups

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

Some aspects of cosheaves on diffeological spaces

We define a notion of cosheaves on diffeological spaces by cosheaves on the site of plots. This provides a framework to describe diffeological objects such as internal tangent bundles, the Poincar'{e} groupoids, and furthermore, homology theories such as cubic homology in diffeology by the language of cosheaves. We show that every cosheaf on a diffeological space induces a cosheaf in terms of t...