Related papers: Normalizers of solvable spherical subgroups

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero…

Let $G$ be a complex reductive algebraic group, $g$ its Lie algebra and $h$ a reductive subalgebra of $g$, $n$ a positive integer. Consider the diagonal actions $G:g^n, N_G(h):h^n$. We study a relation between the algebra $C[h^n]^{N_G(h)}$…

Let $G$ be a finite group and $H$ a normal subgroup. Starting from $G$-spin models, in which a non-Abelian field ${\mathcal{F}}_H$ w.r.t. $H$ carries an action of the Hopf $C^*$-algebra $D(H;G)$, a subalgebra of the quantum double $D(G)$,…

If $G$ is an omega-stable group with a normal definable subgroup $H$, then the Sylow-$2$-subgroups of $G/H$ are the images of the Sylow-$2$-subgroups of $G$.

Let $G$ be a finite group. The aim of this paper is to study the number of solutions $S\subseteq G$ of the equation $\mho^{\{n\}}(S)=L$, where $L$ is a non-empty subset of $G$, $n$ is a positive integer and $\mho^{\{n\}}(S)=\{ s^n \ | \…

In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In this paper, we refine our previous work by considering all finite almost simple groups. In…

Consider a hyperbolic group G and a quasiconvex subgroup H of infinite index. We construct a set-theoretic section s of the quotient map (of sets) from G to G/H such that s(G/H) is a net in G; that is, any element of G is a bounded distance…

We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy…

We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and f is a non-trivial irreducible…

Let G be an exceptional algebraic group defined over an algebraically closed field k of characteristic p>0 and let H be a subgroup of G. Then following Serre we say H is G-completely reducible or G-cr if, whenever H is contained in a…

Given a finite group $G$, we denote by $\nu(G)$ the probability that two randomly chosen elements of $G$ generate a nilpotent subgroup. We prove that if $\nu(G)>1/12,$ then $G$ is solvable.

Let $\sigma =\{\sigma_{i} | i\in I\}$ be a partition of the set $\Bbb{P}$ of all primes and $G$ a finite group. A chief factor $H/K$ of $G$ is said to be $\sigma$-central if the semidirect product $(H/K)\rtimes (G/C_{G}(H/K))$ is a…

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

We prove a natural generalization of Szep's conjecture. Given an almost simple group $G$ with socle not isomorphic to an orthogonal group having Witt defect zero, we classify all possible group elements $x,y\in G\setminus\{1\}$ with $G={\bf…

An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(T_p M) for all p in M, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we…

We continue the analysis of definably compact groups definable in a real closed field $\mathcal{R}$. In [3], we proved that for every definably compact definably connected semialgebraic group $G$ over $\mathcal{R}$ there are a connected…

Suppose that $G$ is a finite, transitive, solvable permutation group acting on a set $S$ with $n$ elements. Let $G_0$ be the stabilizer of a point $\alpha \in \Omega$. Define the rank of a permutation group, denoted $r(G),$ as the number of…

Let $G$ be a connected reductive linear algebraic group over a field $k$. Using ideas from geometric invariant theory, we study the notion of $G$-complete reducibility over $k$ for a Lie subalgebra $\mathfrak h$ of the Lie algebra…

We study groups having the property that every non-cyclic subgroup contains its centralizer. The structure of nilpotent and supersolvable groups in this class is described. We also classify finite $p$-groups and finite simple groups with…

Let Z be an algebraic homogeneous space Z=G/H attached to real reductive Lie group G. We assume that Z is real spherical, i.e., minimal parabolic subgroups have open orbits on Z. For such spaces we investigate their large scale geometry and…