Let $G$ be a finite group. A subgroup $H$ is called $S$-semipermutable in if $HG_p$ = $G_pH$ for any $G_p\in Syl_p(G)$ with $(|H|, p) 1$, where $p$ prime number divisible $|G|$. Furthermore, said to $NH$-embedded there exists normal $T$ of such that $HT$ Hall and $H \cap T \leq H_{\overline{s}G}$, $H_{\overline{s}G}$ the largest contained $H$, $SS$-quasinormal provided supplement $B$ permutes e...

We have studied scalar perturbations as well as fermion perturbations in pure de Sitter space-times. For scalar perturbations we have shown that well-defined quasinormal modes in d-dimensions can exist provided that the mass of scalar field m > d−1 2l . The quasinormal modes of fermion perturbations in three and four dimensional cases have also been investigated. We found that different from ot...

Let $D$ be a division ring with center $F$, and $G$ subnormal or quasinormal subgroup of $D^*$. We show that if is locally solvable, then contained in $F$.

Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra requires solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these...

The intersection graph of quasinormal subgroups a group $G$, denoted by $\Gamma_{\mathrm{q}}(G)$, is defined as follows: the vertex set consists all nontrivial, proper and two distinct vertices $H$ $K$ are adjacent if $H\cap K$ nontrivial. In this paper, we show that when $G$ an arbitrary nonsimple group, diameter $\Gamma_{\mathrm{q}}(G)$ in $\{0,1,2,\infty\}$. Besides, general skew linear grou...

We investigate the evolution of a scalar field propagating in Reissner-Nordström Anti-de Sitter spacetime. Due to the characteristic of spacetime geometry, the radiative tails associated with a massless scalar field propagation have an oscillatory exponential decay. The object-picture of the quasinormal ringing has also been obtained. For small charges, the approach to thermal equilibrium is fa...

We discuss simple integration methods for the calculation of rotating black hole scattering resonances both in the complex frequency plane (quasinormal modes) and the complex angular momentum plane (Regge poles). Our numerical schemes are based on variations of “phase-amplitude” methods. In particular, we discuss the Prüfer transformation, where the original (frequency domain) Teukolsky wave eq...