  We discuss spin-$S$ antiferromagnetic Heisenberg chains with three-spin
interactions, next-nearest-neighbor interactions, and bond alternation. First,
we prove rigorously that there exist parameter regions of the exact dimerized
ground state in this system. This is a generalization of the Majumdar-Ghosh
model to arbitrary $S$. Next, we discuss the ground-state phase diagram of the
models by introducing several effective field theories and the universality
classes of the transitions are described by the level-$2S$ $\mathrm{SU}(2)$
Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the
phase diagrams of $S=1$ and $S=3/2$ systems by using exact diagonalization and
level spectroscopy.
