We show that an element w of a free group F on n generators defines a surjective word map of PSL(2,C)^n onto PSL(2,C) unless w belongs to the second derived subgroup of F. We also describe certain words maps that are surjective on SL(2,C) x SL(2,C). Here C is the field of complex numbers.
We prove that an analogue of Jordans theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of algebraic surfaces. This gives a positive answer to a question of Vladimir L. Popov.
