Abstract
We define a class of •-varieties of algebras and prove that the tame automorphism group of a free algebra of rank two of any •-variety of algebras over a field admits an amalgamated free product structure.In particular, the automorphism group of a free right-symmetric algebra of rank two admits an amalgamated free product structure.Using this structure, we prove that any locally finite group of automorphisms of this algebra is conjugate to a subgroup of affine or triangular automorphisms.This implies that any reductive group of automorphisms of a two-generated free right-symmetric algebra is linearizable and any locally nilpotent derivation of this algebra is triangulable over a field of characteristic zero.All of these results are true for free commutative and free non-associative algebras of rank two.