In this paper we find a necessary and sufficient condition for a finite nilpotent group to have an abelian central automorphism group.

We study extremal properties of the determinant of the Laplacian in the Bergman metric on the moduli space of compact genus two Riemann surfaces. By a combination of analytical and numerical methods we identify four non-degenerate critical points of this function and compute the signature of the Hessian at these points. The curve with the maximal number of automorphisms (the Burnside curve) tur...

Bhargava has given a formula, derived from a formula of Serre, computing a certain count of extensions of a local field, weighted by conductor and by number of automorphisms. We interpret this result as a counting formula for permutation representations of the absolute Galois group of the local field, then speculate on variants of this formula in which the role of the symmetric group is played ...

Introduction: Research evidence indicates that maladaptive reorganization of the brain plays a critical role in amplifying pain experiences and pain chronification; there is, however, no clear evidence of change in brain wave activity among patients with chronic low back pain (CLBP). The objective of this study was to assess brain wave activity in patients with CLBP, compared to healthy control...

We study z-automorphisms of the polynomial algebra K[x, y, z] and the free associative algebra K〈x, y, z〉 over a field K, i.e., automorphisms which fix the variable z. We survey some recent results on such automorphisms and on the corresponding coordinates. For K〈x, y, z〉 we include also results about the structure of the z-tame automorphisms and algorithms which recognize z-tame automorphisms ...