Following Malcev [5], we will call a subgroup M of a group G finitely separable if for any element g ∈ G, not belonging to M, there exists a homomorphism φ of group G onto some finite group X such that gφ / ∈Mφ. This is equivalent to the statement that for any element g ∈ G \M, there exists a normal subgroup N of finite index in G such that g / ∈MN . A group G is subgroup separable if each of i...

For groups of diffeomorphisms $\T^2$ containing an Anosov diffeomorphism, we give a complete classification for polycyclic Abelian-by-Cyclic group actions on up to both topological conjugacy and smooth under mild assumptions. Along the way, also prove Tits alternative type theorem some $\T^2$.

We prove that any two continuous minimal (topologically free) actions of the infinite dihedral group on an compact Hausdorff space are continuously orbit equivalent only if they conjugate. also show above fails we replace by certain other virtually cyclic groups, e.g., direct product integer with non-abelian finite simple group.

Topological indices are mathematical descriptors for molecular structures. These used to describe physico-chemical properties such as solubility, shape and weight. In this paper, we present distance-based topological Wiener index hyper-Wiener by using Hosoya polynomial inverse graphs associated with finite cyclic group. Also, have found eccentricity based of