  We study a family of Thompson-like groups built as rearrangement groups of
fractals from [BF19], each acting on a Wa\.zewski dendrite. Each of these is a
finitely generated group that is dense in the full group of homeomorphisms of
the dendrite (studied in [DM19]) and has infinite-index finitely generated
simple commutator subgroup, with a single possible exception. More properties
are discussed, including finite subgroups, the conjugacy problem, invariable
generation and existence of free subgroups. We discuss many possible
generalizations, among which we find the Airplane rearrangement group $T_A$.
Despite close connections with Thompson's group $F$, dendrite rearrangement
groups seem to share many features with Thompson's group $V$.
