Search results for "Solvability"
showing 4 items of 4 documents
Powers of conjugacy classes in a finite groups
2020
[EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability concerning the case in which the power of a conjugacy class is a union of one or two conjugacy classes. Moreover, we show that the above conditions can be determined through the character table of the group.
ON SOLVABILITY OF THE DAMPED FUČÍK TYPE PROBLEM WITH INTEGRAL CONDITION
2014
The solvability results are established for the boundary value problem with a damping term , x(0) = 0, where x + = max{x, 0}, x - = max{-x, 0}, h is a bounded nonlinearity, µ, λ real parameters. The existence results are based of the knowledge of the Fučík type spectrum for the problem with h ≡ 0
Uniform rectifiability implies Varopoulos extensions
2020
We construct extensions of Varopolous type for functions $f \in \text{BMO}(E)$, for any uniformly rectifiable set $E$ of codimension one. More precisely, let $\Omega \subset \mathbb{R}^{n+1}$ be an open set satisfying the corkscrew condition, with an $n$-dimensional uniformly rectifiable boundary $\partial \Omega$, and let $\sigma := \mathcal{H}^n\lfloor_{\partial \Omega}$ denote the surface measure on $\partial \Omega$. We show that if $f \in \text{BMO}(\partial \Omega,d\sigma)$ with compact support on $\partial \Omega$, then there exists a smooth function $V$ in $\Omega$ such that $|\nabla V(Y)| \, dY$ is a Carleson measure with Carleson norm controlled by the BMO norm of $f$, and such th…
Some problems about products of conjugacy classes in finite groups
2020
[EN] We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect some problems that have only been partially solved.