# Houston Problem Book Problem 10

**Problem 10 (HPB):** Suppose $D$ is a dendroid, $S$ is compact, finitely generated commutative semigroup of monotone surjections on $D$ which has a fixed end point. Does $S$ have another fixed point? (Asked by L.E. Ward, 20 October 1971)

**Answer:** Yes, even for $\lambda$-dendroids (W.J. Gray and S. Williams, Bull. Polish Acad. Sci. 27 (1979), 599-604)