Which words spell ``almost nilpotent''? (Q1965252)

The author introduces a special set of words (so called efficient words) and proves that there exists a function \(f=f(N)\) such that any finite group satisfying an identity of length \(N\) defined by an efficient word is nilpotent-of-class-at-most-\(f\)-by-exponent-at-most-\(f\). Conversely, a group which is nilpotent-of-class-\(c\)-by-exponent-at-most-\(c\) satisfies an efficient law, whose length is \(c\)-bounded. Related results are discussed. Some open questions are stated.