Spin groups of super metrics and a theorem of Rogers

Some of our results were known to DeWitt (1984) using formal Grassmann series and others were known by Rogers using finitely many Grassmann generators and passing to a direct limit. We work exclusively in the category of G∞ supermanifolds with G∞ mappings. Our supernumbers are infinite series of products of Grassmann generators subject to convergence in the ℓ1 norm introduced by Rogers (1980, 2007).