This paper presented the synthesis of Ag nanoparticles (Ag NPs) by the chemical reduction method which is simple and environmentally friendly. Silver nitrate, hydroxypropylmethyl cellulose (HPMC), and glucose were used as silver precursors, protective agents, and reducing agents, respectively. The effects of AgNO 3 concentration, glucose concentration, HPMC content, reaction time, and reaction temperature on the formation of Ag NPs were investigated. The properties of Ag NPs were analyzed by transmission electron microscopy (TEM), ultraviolet-visible (UV-Vis) spectroscopy, and X-ray diffraction (XRD). The results indicated that when the HPMC content was 0.01%, AgNO 3 concentration was 0.05 M and glucose reducing agent concentration was 0.4%, the best reaction occurred in 9 hours at 90 o C. The Ag NPs prepared under HPMC protection possessed a face-centered cubic crystal structure (FCC), a spherical shape having average sizes in the range of 8 − 12 nm. The Ag colloidal solution had a suitable zeta potential (-37.21 mV) to maintain the stability and to avoid the agglomeration of Ag NPs. In addition,the paper proposed a method to indirectly determine the Ag NPs content through the separation of Ag NPs from the colloidal solution by coagulation, using the electrolyte Al(NO 3 ) 3 .9H 2 O.

Let $F$ be a field and let $n$ be a natural number greater than $1$. The aim of this paper is to prove that if $F$ contains at least three elements, then every matrix in the special linear group $\mathrm{SL}_n(F)$ is a product of at most two commutators of involutions.

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