# Hyperfield extensions, characteristic one and the Connes-Consani plane connection

@article{Thas2014HyperfieldEC, title={Hyperfield extensions, characteristic one and the Connes-Consani plane connection}, author={Koen Thas}, journal={arXiv: Group Theory}, year={2014} }

Inspired by a recent paper of Alain Connes and Catherina Consani which connects the geometric theory surrounding the elusive field with one element to sharply transitive group actions on finite and infinite projective spaces ("Singer actions"), we consider several fudamental problems and conjectures about Singer actions. Among other results, we show that virtually all infinite abelian groups and all (possibly infinitely generated) free groups act as Singer groups on certain projective planes…

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