Local Moufang sets and PSL_2 over a local ring

摘要

We introduce local Moufang sets as a generalization of Moufang sets. Wepresent a method to construct local Moufang sets from only one root group andone permutation. We use this to describe $\mathsf{PSL}_2$ over a local ring asa local Moufang set, and give necessary and sufficient conditions for a localMoufang set to be of this form.