The small index property for algebras (Q1587008)

Let \(M\) be an infinite countable model with automorphism group \(G\), and let \(Y\) be a finite subset of \(M\) with pointwise stabilizer \(G_Y\). If every subgroup of \(G\) with index less than the cardinality of the continuum contains some \(G_Y\) then \(G\) is said to possess the small index property. In the article under review, the author shows that the free Lie algebra of countably infinite rank over a finite or countable field possesses the small index property. The methods used are based on the article by \textit{R.~M.~Bryant} and \textit{D.~M.~Evans} [J. Lond. Math. Soc., II. Ser. 55, No. 2, 363-369 (1997; Zbl 0867.20032)].