Torsors under some group schemes of order pn

Let R be a complete dvr with perfect residue field k of characteristic p > 0. Let {G(lambda))lambda is an element of R be the class of R-affine, commutative, smooth of relative dimension one group schemes generically isomorphic to G(m). Let G := {G(lambda,n))(lambda is an element of R,n is an element of N) be the class of finite flat commutative group schemes of order p(n) defined as kernels of the isogenies phi(lambda,n):G(lambda)-> G((lambda pn)). We provide an explicit description of torsors over R-schemes under the group schemes G(lambda) and G(lambda,n). (C) 2007 Elsevier Inc. All rights reserved.