  We present exact models for an antiferromagnetic S=1 spin chain describing
trimerization as well as for an antiferromagnetic S=3/2 spin chain describing
tetramerization. These models can be seen as generalizations of the
Majumdar-Ghosh model. For both models, we provide a local Hamiltonian and its
exact three- or four-fold degenerate ground state wavefunctions, respectively.
We numerically confirm the validity of both models using exact diagonalization
and discuss the low lying excitations.
