We make a connection between the structure of bidisc and distinguished subgroup its automorphism group. The group bidisc, as we know, is dimension six acts transitively. observe that it contains isomorphic to open unit disc this partitions into complex curve family strongly pseudo-convex hypersurfaces are non-spherical CR-manifolds. Our work reverses process shows any 2-dimensional Kobayashi-hy...

A generalized tetrahedron group is defined to be a group admitting the following presentation: 〈x, y, z | x = y = z = W p 1 (x, y) = W q 2 (y, z) = W r 3 (x, z) = 1〉, 2 ≤ l,m, n, p, q, r, where each Wi(a, b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized tri...

A generalized tetrahedron group is defined to be a group admitting the following presentation: 〈x, y, z | xl = ym = zn = W p 1 (x, y) = W q 2 (y, z) = W r 3 (x, z) = 1〉, 2 ≤ l, m, n, p, q, r, where each Wi(a, b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized...

Let F and r' be lattices, and (p and 4> one-parameter subgroups of the connected Lie groups G and G'. If one of the following conditions (a), (b), or (c) hold, Theorem A states that if the induced flows on the homogeneous spaces G/T and G'/Y' are topologically equivalent, then they are topologically equivalent by an affine map. (a) G and G' are one-connected and nilpotent. (b) G and G' are one-...

We prove that cyclic subgroup separability is preserved under exponential completion for groups belong to a class includes all coherent RAAGs and toral relatively hyperbolic groups; we do so by exploiting the structure of these completions as iterated free products with commuting subgroups. From this deduce subgroups limit over are separable, answering question Casals-Ruiz, Duncan, Kazachkov. a...

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...

Using an isomorphism between Hilbert spaces L and l 2 we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term difference equation. Technique of intertwining operators is applied to creating new families of exactly solvable Jacobi matrices. It is shown that any thus obtained Jacobi m...

It is proved that the free boundary problem for two phase viscous compressible and incompressible fluids in spaces $$ {W}_p^{2+l,1+l/2} (QT) with p > 2, l ∈ (1/p, 2/p), solvable locally time.

A subset X of a finite group G is said to be prime-power-independent if each element in has prime power order and there no proper Y with 〈Y,Φ(G)〉=〈X,Φ(G)〉, where Φ(G) the Frattini subgroup G. Bpp all generating sets for have same cardinality. We prove that, Bpp, then solvable. Pivoting on some recent results Krempa Stocka (2014); (2020), this yields complete classification Bpp-groups.

A result of Bridson, Howie, Miller and Short states that if $S$ is a subgroup type $FP_{n}(\mathbb{Q})$ the direct product $n$ limit groups over free groups, then virtually groups. Furthermore, they characterise finitely presented residually In this paper these results are generalised to Droms right-angled Artin RAAGs with property all their generated subgroups again RAAGs. addition, we show co...