Abstract: Parafree Lie algebras are algebras that are residually nilpotent and satisfy the property that their quotients by the terms of the lower central series are isomorphic to the corresponding quotients of a free Lie algebra. There are many nonfree parafree Lie algebras and they all have many properties in common with free Lie algebras. In this paper, our main goal is to investigate the free product of parafree Lie algebras. In particular, we prove that a finite number of free factors of a parafree Lie algebra are parafree.

Keywords: Free Lie algebras, Parafree Lie algebras, Free Product, Free Factors

| DOI: 10.17148/IARJSET.2020.7201