Zassenhaus conjecture for central extensions of S5

We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S5 and for the general linear group GLð2; 5Þ. The first result, together with others from the literature, settles the conjugacy question for units of prime-power order in the integral group ring of a finite Frobenius group

Distribution Dynamics in the US. A spatial perspective.

It is quite common in cross-sectional convergence analyses that data exhibit strong spatial dependence. While the literature adopting the regression approach is now fully aware that neglecting this feature may lead to inaccurate results and has therefore suggested a number of statistical tools for addressing the issue, research is only at a very initial stage within the distribution dynamics approach. In particular, in the continuous state-space framework, a few authors opted for spatial pre-filtering the data in order to guarantee the statistical properties of the estimates. In this paper, we follow an alternative route that starts from the idea that spatial dependence is not just noise but can be a substantive element of the data generating process. In particular, we develop a tool that, building on a mean-bias adjustment procedure established in the literature, explicitly allows for spatial dependence in distribution dynamics analysis thus eliminating the need for pre-filtering. Using this tool, we then reconsider the evidence on convergence across US states