The maximumof the degree of nonholonomy of the control system attached to a kinematic model for the car with n trailers is F n+3 where F n is the n th term of the Fibonacci's sequence (F 0 = 0; F 1 = 1; F n+2 = F n+1 + F n ; n 0). This value is obtained if and only if each trailer (except for the last one) is perpendicular to the previous one.

In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎w...

Let $G$ be a finite $p$-group. In this paper we obtain bounds for the exponent of non-abelian tensor square $G \otimes G$ and $\nu(G)$, which is certain extension by \times G$. particular, bound $\exp(\nu(G))$ in terms $\exp(\nu(G/N))$ $\exp(N)$ when admits some specific normal subgroup $N$. We also establish $\exp(G G)$ $\exp(G)$ either nilpotency class or coclass group $G$, improving existing...