Free *-subalgebras of C*-algebras

The aim of this work is to study the existence of free *-subalgebras in C*-algebras. The Kurosh–Levitzky Problem and related conjectures of Makar-Limanov are answered in the context of C*-algebras. In particular, we characterize and study the existence of free non-Abelian *-subalgebras with two self-adjoint contractions in finitely-generated C*-algebras. C*-algebras having linear growth are shown to be subhomogeneous.