In this paper we study the structure of locally solvable, solvable, locally nilpotent, and nilpotent maximal subgroups of skew linear groups. In [S. Akbari et al., J. Algebra 217 (1999) 422–433] it has been conjectured that if D is a division ring and M a nilpotent maximal subgroup of D∗, then D is commutative. In connection with this conjecture we show that if F [M]\F contains an algebraic ele...

Let nand k be positive integers. We say that a group G satisfies the condition £(n) (respectively, £dn)) if and only if any set with n + 1 elements of G contains two distinct elements x, y such that [x,t y] = 1 for some positive integer t = t(x, y) (respectively, [X,k y] = 1). Here we study certain groups satisfying these conditions. We prove that if G is a finite group satisfying the condition...

Abstract A parameter $c_{0}\in {\mathbb {C}}$ in the family of quadratic polynomials $f_{c}(z)=z^{2}+c$ is a critical point period n multiplier if map $f_{c_{0}}$ has periodic orbit , whose multiplier, viewed as locally analytic function c vanishing derivative at $c=c_{0}$ . We study accumulation set ${\mathcal X}$ points multipliers $n\to \infty $ This complements equidistribution result for t...

We construct embeddings Yn,τ → Hilb (Στ ) for each of the classical Lie algebras sp2m(C), so2m(C), and so2m+1(C). The space Yn,τ is the fiber over a point τ ∈ h/W of the restriction of the adjoint quotient map χ : g → h/W to a suitably chosen transverse slice of a nilpotent orbit. These embeddings were discovered for sl2m(C) by Ciprian Manolescu. They are related to the symplectic link homology...

We study asymptotically flat stationary solutions of four-dimensional supergravity theories via the associated G/H pseudo-Riemannian non-linear sigma models in three spatial dimensions. The Noether charge C associated to G is shown to satisfy a characteristic equation that determines it as a function of the four-dimensional conserved charges. The matrix C is nilpotent for non-rotating extremal ...

is soluble for every pG.m and every gGG. Similarly we call a group G a Dor-group if the equation (1) (above) is not only soluble, but uniquely soluble. The class of Fur-groups and the class of Dor-groups will be denoted respectively by Em and Dm. Clearly Em~2)Dm. There is a less trivial relationship between these two classes of groups. If we denote by ©(C) the class of groups which occur as hom...

We exhibit pseudo Riemannian manifolds which are Szabó nilpotent of arbitrary order, or which are Osserman nilpotent of arbitrary order, or which are Ivanov-Petrova nilpotent of order 3.

Let G = Sp(2n,C) be a complex symplectic group. In the companion paper [math.AG/0601154], we introduced a (G × C × C)-variety N, which we call the exotic nilpotent cone. In this paper, we realize the Hecke algebra H of type C n with unequal parameters via equivariant algebraic K-theory in terms of the geometry of N. This enables us to establish a Deligne-Langlands type classification of “non-cr...

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

In this paper we introduce controlled *-g-frame and *-g-multipliers in Hilbert C*-modules and investigate the properties. We demonstrate that any controlled *-g-frame is equivalent to a *-g-frame and define multipliers for (C,C')- controlled*-g-frames .