Products of primes in conjugacy class sizes and irreducible character degrees

We prove that if the product pq of distinct primes p and q divides the degree of some irreducible complex character of a finite group G, then pq divides the size of some conjugacy class of G.     

A few simple rules governing hydrogenation of graphene dots

We investigated binding of hydrogen atoms to small polycyclic aromatic hydrocarbons (PAHs)--i.e., graphene dots with hydrogen-terminated edges--using density functional theory and correlated wavefunction techniques. We considered a number of PAHs with three to seven hexagonal rings and computed binding energies for most of the symmetry unique sites, along with the minimum energy paths for significant cases. The chosen PAHs are small enough to not present radical character at their edges, yet show a clear preference for adsorption at the edge sites which can be attributed to electronic effects. We show how the results, as obtained at different levels of theory, can be rationalized in detail with the help of a few simple concepts derivable from a tight-binding model of the π electrons.     

Finite groups whose noncentral class sizes have the same p-part for some prime p

We describe the structure of the finite groups in which the sizes of noncentral conjugacy classes have the same p-part, for some prime p. We prove that they are solvable, they have a normal p-complement and their Fitting length is at most three.     

Dynamic analysis of the ball-racket impact in the game of tennis

A new approach to the study of the impact phase in tennis is presented. It allows, in particular, an analysis of the forces transmitted to the arm joints from the racket and calculation of the speed variation of ball and racket subsequent to their impact.

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Sommario In questo lavoro viene proposto un nuovo approccio allo studio della fase d'urto racchetta-pallina nel gioco del tennis. Esso consente, in particolare, di analizzare le sollecitazioni trasmesse dalla racchetta alle articolazioni del braccio, e calcolare la variazione delle velocita' della pallina e della racchetta provocate dal loro impatto.

     

Finite groups with small conjugacy classes

We study finite groups G in which the number of distinct prime divisors of the length of the conjugacy classes is at most three. In particular we prove, under this condition, a conjecture of B. Huppert on the number of prime divisors of ÷G/Z(G)÷.