Y. Berkovich has proposed to classify nonabelian finite pgroups G of exponent > p which have exactly p maximal abelian subgroups of exponent > p and this was done here in Theorem 1 for p = 2 and in Theorem 2 for p > 2. The next critical case, where G has exactly p + 1 maximal abelian subgroups of exponent > p was done only for the case

Using the fact that all groups of exponent 3 are nilpotent, we show that every sharply 2-transitive permutation group whose point stabilizer has exponent 3 or 6 is finite.

A quasiperiodic word is, here, a finite or infinite word that can be obtained by concatenations or overlaps of a given finite word, called a quasiperiod of the whole word. For instance, aba is a quasiperiod of the Fibonacci word. It is an immediate observation that any quasiperiodic word contains an overlap. Thus its critical exponent is greater than 2. What is the minimal critical exponent of ...

The fastest known algorithm for factoring univariate polynomials over finite fields is the KedlayaUmans [13] (fast modular composition) implementation of the Kaltofen-Shoup algorithm [12, § 2]. It is randomized and takes Õ(n3/2 log q+n log2 q) time to factor polynomials of degree n over the finite field Fq with q elements. A significant open problem is if the 3/2 exponent can be improved. We st...

We study the dynamics of a driven interface in a twodimensional random-field Ising model close to the depinning transition at small but finite temperatures T using Glauber dynamics. A square lattice is considered with an interface initially in (11)-direction. The drift velocity v is analyzed using finite size scaling at T = 0 and additionally finite temperature scaling close to the depinning tr...

We consider the one-sided exit problem for (fractionally) integrated random walks and Lévy processes. We prove that the rate of decrease of the non-exit probability – the so-called survival exponent – is universal in this class of processes. In particular, the survival exponent can be inferred from the (fractionally) integrated Brownian motion. This, in particular, extends Sinai’s result on the...

Lagrangian coherent structures play an important role in the analysis of unsteady vector fields because they represent the timedependent analog to vector field topology. Nowadays, they are often obtained as ridges in the finite-time Lyapunov exponent of the vector field. However, one drawback of this quantity is its very high computational cost because a trajectory needs to be computed for ever...