  Let R be a discrete valuation ring with residue field of characteristic p>0.
Let K be its fraction field. We prove that any finite and flat R-group scheme,
isomorphic to \mu_{p^2,K} on the generic fiber, is the kernel in a short exact
sequence which generically coincides with the Kummer sequence. We will
explicitly describe and classify such models. In the appendix X. Caruso shows
how to classify models of \mu_{p^2,K}, in the case of unequal characteristic,
using the Breuil-Kisin theory.
