Using classification theorems of simple groups, we give a proof of a conjecture on factorized finite groups which is an extension of a well known theorem due to P. Hall.

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial ...

In this work we study some properties of the differential complex associated to a locally integrable (involutive) structure acting on forms with Gevrey coefficients. Among other results we prove that, for such complexes, ...

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and ...

We studied the solvability of the algebra which satisfies the polynomial identity (x 2)2 = 0. We believe that, if A is a finite dimensional commutative algebra over a field F of characteristic not 2 which satisfies (x 2)2 ...

Global solvability on the two-torus of a first order differential operator with complex coefficients is investigated. Diophantine properties of the coefficients are linked to the solvability.

We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the ...

We study commutative right-nilalgebras of right-nilindex four satisfying the identity (b(aa))a = b((aa)a). Ourmainresultisthatthese algebras are solvable and not necessarily nilpotent. Our results require characteristic 6≠2, 3, 5.

Given a lattice Gamma subset of SOL, we show there is a uniformly discrete coarsely dense subset D subset of Gamma that is not bi-Lipschitz equivalent to Gamma. We also prove similar results for lattices in certain higher ...

The goal of this paper is study the global solvability of a class of complex vector fields of the special form L = partial derivative/partial derivative t + (a + ib)(x)partial derivative/partial derivative x, a, b epsilon ...