Improving Thompson's Conjecture for Suzuki Groups

Let G be a finite group and cs(G) be the set of conjugacy class sizes of G. In 1987, J. G. Thompson conjectured that, if G is a finite group with Z(G) = 1 and M is a nonabelian simple group satisfying that cs(G) = cs(M), then G ? M. This conjecture has been proved for Suzuki groups in [5 Guiyun, C. (1996). On Thompson's conjecture. J. Algebra 185(1):184–193.[Crossref], [Web of Science ®] , [Google Scholar]]. In this article, we improve this result by proving that, if G is a finite group such that cs(G) = cs(Sz(q)), for q = 2^2m+1, then G ? Sz(q) × A, where A is abelian. We avoid using classification of finite simple groups in our proofs.     

Assessment of two analytical approaches in some nonlinear problems arising in engineering sciences

In this research, two powerful analytical methods are introduced to handle nonlinear good Boussinesq, heat transfer and coupled Burgers' equations. One is the homotopy-perturbation method (HPM) and the other is the variational iteration method (VIM). VIM is used to construct correction functionals using general Lagrange multipliers identified optimally via the variational theory. HPM converts a difficult problem into a simple one, which can be easily handled. The results attained in this paper confirm the idea that HPM and VIM are powerful mathematical tools and that they can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.     

Structure of normal subgroups with three G-class sizes

Let G be a finite group and N be a normal subgroup of G. Suppose that the set of G-conjugacy class sizes of N is {1, m, n}, with m?<?n and m does not divide n. In this paper, we show that N is solvable, and we determine the structure of these subgroups.     

Waste-grass-mediated green synthesis of silver nanoparticles and evaluation of their anticancer,antifungal and antibacterial activity

Grass waste was used for transform an inexpensive waste into health. Silver nanoparticles (AgNPs) have been synthesized using waste material (dried grass). The average size of silver nanoparticles observed in transmission electron images was estimated to be about 15?nm. The anticancer, antifungal and antibacterial effect of AgNPs were studied in vitro. The minimum inhibitory concentration of AgNPs against Pseudomonas aeruginosa and Acinetobacter baumannii was calculated about 3?µg/ml. The highest level of inhibitory effect of AgNPs against Fusarium solani was close to 90% at a concentration of 20?μg/ml of AgNPs. An inhibitory effect on the cancer cell growth is reach, by increasing the concentration of AgNPs to 5?µg/ml; the cancer cells’ survival decreases about 30%. Western results showed that the expression of Cyclin D1 protein of MCF-7 cell line decreased after treatment with the effective concentration of AgNPs.     

Quasirecognition by prime graph of the simple group <Superscript>2</Superscript><Emphasis Type="Italic">F</Emphasis><Subscript>4</Subscript>(<Emphasis Type="Italic">q</Emphasis>)

As the main result, we show that if G is a finite group such that Γ(G) = Γ(² F ₄(q)), where q = 2^2m+1 for some m ≧ 1, then G has a unique nonabelian composition factor isomorphic to ² F ₄(q). We also show that if G is a finite group satisfying |G| =|² F ₄(q)| and Γ(G) = Γ(² F ₄(q)), then G ≅ ² F ₄(q). As a consequence of our result we give a new proof for a conjecture of W. Shi and J. Bi for ² F ₄(q). The third author was supported in part by a grant from IPM (No. 87200022).     

Facile Biosynthesis of Silver Nanoparticles Using <Emphasis Type="Italic">Descurainia sophia</Emphasis> and Evaluation of Their Antibacterial and Antifungal Properties

The objective of the present study was to evaluate efficiency of silver nanoparticles (Ag-NPs) biosynthesis using Descurainia sophia as a novel biological resource. The resulting synthesized Ag-NPs were characterized using UV visible spectroscopy, X-ray diffraction, transmission electron microscopy and dynamic light scattering (DLS). The UV–Vis spectra gave surface plasmon resonance at ~420 nm. TEM images revealed formation spherical shaped Ag-NPs with size ranged from to 1–35 nm. DLS confirmed uniformity of the synthesized Ag-NPs with an average size of ~30 nm. Following, the antibacterial and antifungal activities of the synthesized Ag-NPs were investigated. The concentration 25 µg/ml of the Ag-NPs showed maximum inhibitory effect on mycelium growth of Rhizoctonia solani (More than 86 % inhibition), followed by 15 µg/ml (55 % inhibition) and 10 µg/ml (63 % inhibition). The minimum inhibitory concentration and minimum bactericidal concentration of Ag-NPs against Agrobacterium tumefaciens (strain GV3850) and A, rhizogenes (strain 15843) were 4 and 8 µg/ml, respectively. The Ag-NPs were stable in vitro for 3 months without any precipitation or decrease of antifungal effects. Finally, it could be concluded that D. sophia can be used as an effective method for biosynthesis of nanoparticles, especially Ag-NPs.