On the quasi group of a cubic surface over a finite field
  We construct nontrivial homomorphisms from the quasi group of some cubic surfaces over $\bbF_{\!p}$ into a group. We show experimentally that the homomorphisms constructed are the only possible ones and that there are no nontrivial homomorphisms in the other cases. Thereby, we follow the classification of cubic surfaces, due to A. Cayley. 
Andreas-Stephan Elsenhans, J\"org Jahnel
math.AG