  In this paper, we study sheets of symmetric Lie algebras through their
Slodowy slices. In particular, we introduce a notion of slice induction of
nilpotent orbits which coincides with the parabolic induction in the Lie
algebra case. We also study in more details the sheets of the non-trivial
symmetric Lie algebra of type G2. We characterize their singular loci and
provide a nice desingularisation lying in so7.
