Let p be any prime. P n a Sylow -subgroup of the symmetric group S . ϕ and ψ linear characters let N normaliser in In this article we show that inductions to are equal if, only –conjugate. This is an analogue for groups result Navarro -solvable groups.

Let [Formula: see text] be a finite group and fixed prime divisor of text]. We prove that if every maximal subgroup is nilpotent, or normal, has text]-order, then (1) solvable; (2) Sylow tower; (3) there exists at most one such neither text]-nilpotent nor text]-closed.

We discuss distortion of solvable linear groups over a locally compact field and provide necessary and sufficient conditions for a subgroup to be undistorted when the field is of characteristic zero.

This note aims to clarify what conditions on a connected Lie group G imply that its maximal connected normal solvable subgroup R intersects each lattice of G as a lattice in R.

Let $ G be the group of orientation-preserving isometries a rank-one symmetric space X non-compact type. We study local rigidity certain actions solvable subgroup \Gamma \subset on boundary $, which is diffeomorphic to sphere. When quaternionic hyperbolic or Cayley hyperplane, action we constructed locally rigid.

Abstract Let p be a prime. A pro- group G is said to 1-smooth if it can endowed with continuous representation $\theta \colon G\to \mathrm {GL}_1(\mathbb {Z}_p)$ such that every open subgroup H of , together the restriction \vert _H$ satisfies formal version Hilbert 90. We prove contains unique maximal closed abelian normal subgroup, in analogy result by Engler and Koenigsmann on Galois groups ...

Let G be a finite group and let K = x the conjugacy class of an element G. In this paper, it is proved that if N normal subgroup such coset union ? 1 (the inverse x), then ? ? are solvable. As application, we prove there exists natural number n ? 2 ? ,

Given a short exact sequence of groups with certain conditions, 1 → F → G → H → 1, we prove that G has solvable conjugacy problem if and only if the corresponding action subgroup A Aut(F ) is orbit decidable. From this, we deduce that the conjugacy problem is solvable, among others, for all groups of the form Z2 Fm, F2 Fm, Fn Z, and Zn A Fm with virtually solvable action group A GLn(Z). Also, w...

Abstract. Let L = divA∇ be a real, symmetric second order elliptic operator with bounded measurable coefficients. Consider the elliptic equation Lu = 0 in a bounded Lipschitz domain Ω of R. We study the relationship between the solvability of the L Dirichlet problem (D)p with boundary data in L(∂Ω) and that of the L regularity problem (R)q with boundary data in W (∂Ω), where 1 < p, q < ∞. It is...

The following structure theorems are proved: An orbit of a real solvable Lie group in projective space that is a complex submanifold is isomorphic to C x (C*)m x Í2 , where Í2 is an open orbit of a real solvable Lie group in a projective rational variety. Also, any homogeneous space of a complex Lie group that is isomorphic to C" can be realized as an orbit in some projective space. As a conseq...