Let A be a finite dimensional associative algebra with derivations over field of characteristic zero, i.e., an whose structure is enriched by the action Lie L derivations, and let cnL(A), n≥1, its differential codimension sequence. Such sequence exponentially bounded expL⁡(A)=limn→∞⁡cnL(A)n integer that can computed, called PI-exponent A. In this paper we prove for any L, expL⁡(A) coincides exp...

This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free...