Torsion in free centre-by-nilpotent-by-abelian Lie rings of rank 2

Abstract

For c ≥ 2, the free centre-by-(nilpotent-of-class-c-1)-by abelian Lie ring on a set X is the quotient L/[(L ′ ) c , L] where L is the free Lie ring on X, and (L ′ ) c denotes the cth term of the lower central series of the derived ideal L ′ = L 2 of L. In this paper we give a complete description of the torsion subgroup of its additive group in the case where |X| = 2 and c is a prime number.