University of Isfahan International Journal of Group Theory 2251-7650 7 2 2018 06 01 On the dimension of the product $[L_2,L_2,L_1]$‎ in free Lie algebras 45 50 21481 10.22108/ijgt.2017.21481 EN Nil Mansuroğlu Ahi Evran University Journal Article 2016 11 21 Let $L$ be a free Lie algebra of rank $r\geq2$ over a field $F$ and let $L_n$ denote the degree $n$ homogeneous component of $L$‎. ‎By using the dimensions of the corresponding homogeneous and fine homogeneous components of the second derived ideal of free centre-by-metabelian Lie algebra over a field $F$‎, ‎we determine the dimension of $[L_2,L_2,L_1]$‎. ‎Moreover‎, ‎by this method‎, ‎we show that the dimension of $[L_2,L_2,L_1]$ over a field of characteristic $2$ is different from the dimension over a field of characteristic other than $2$.<br /><br /> https://ijgt.ui.ac.ir/article_21481_0b392ad1ffab7cd79272442ecc91712c.pdf