  Each orthogonal group O(n) has a nontrivial GL(1)-extension, which we call
GPin(n). The identity component of GPin(n) is the more familiar GSpin(n), the
general Spin group. We prove that the restriction to GPin(n-1) of an
irreducible admissible representation of GPin(n) over a nonarchimedean local
field of characteristic zero is multiplicity free and also prove the analogous
theorem for GSpin(n). The case for GPin(n) is the analogue of the theorem for
O(n) proven by Aizenbud, Gourevitch, Rallis and Schiffmann, and the case for
GSpin(n) the one for SO(n) by Waldspurger.
