let $g$ be a finite group‎. ‎we say that $g$ has emph{spread} r if for any set of distinct non-trivial elements of $g$ $x:={x_1,ldots‎, ‎x_r}subset g^{#}$ there exists an element $yin g$ with the property that $langle x_i,yrangle=g$ for every $1leq ileq r$‎. ‎we say $g$ has emph{exact spread} $r$ if $g$ has spread $r$ but not $r+1$‎. ‎the spreads of finite simple groups and their decorations ha...

here we consider all finite non-abelian 2-generator $p$-groups ($p$ an odd prime) of nilpotency class two and study the probability of having $n^{th}$-roots of them. also we find integers $n$ for which, these groups are $n$-central.

let $g$ be a $p$-group of order $p^n$ and $phi$=$phi(g)$ be the frattini subgroup of $g$. it is shown that the nilpotency class of $autf(g)$, the group of all automorphisms of $g$ centralizing $g/ fr(g)$, takes the maximum value $n-2$ if and only if $g$ is of maximal class. we also determine the nilpotency class of $autf(g)$ when $g$ is a finite abelian $p$-group.

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

Wang M, Zhang W, Crisostomo P, Markel T, Meldrum KK, Fu XY, Meldrum DR. Endothelial STAT3 plays a critical role in generalized myocardial proinflammatory and proapoptotic signaling. Am J Physiol Heart Circ Physiol 293: H2101–H2108, 2007. First published August 3, 2007; doi:10.1152/ajpheart.00125.2007.—Signal transducer and activator of transcription (STAT) 3 is involved in mediating a broad ran...

We report a numerical investigation of surface plasmon (SP) propagation in ordered and disordered linear chains of metal nanospheres. In our simulations, SPs are excited at one end of a chain by a near-field tip. We then find numerically the SP amplitude as a function of propagation distance. Two types of SPs are discovered. The first SP, which we call the ordinary or quasistatic, is mediated b...

As explained in a companion piece, there is a curious anomaly in the law of punitive damages. Jurors assess punitive damages in an amount that they believe will best “punish” the defendant. But, in fact, business defendants are not always punished to the degree that the jury intends. This is because jurors do not take into account the fact that these businesses are allowed to deduct their punit...