Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16121220201201Understanding Wall's theorem on dependence of Lie relators in Burnside groups12914310752410.30504/jims.2020.107524ENM.Vaughan-LeeChrist Church, University of Oxford,
Oxford, OX1 1DP, England.Journal Article20200325G.E. Wall [J. Algebra 104 (1986), no. 1, 1--22; Lecture Notes in Mathematics, pp. 191--197, 1456, Springer-Verlag, Berlin, 1990] gave two different proofs of a remarkable result about the multilinear Lie relators satisfied by groups of prime power exponent $q$. He showed that if $q$ is a power of the prime $p$, and if $f$ is a multilinear Lie relator in $n$ variables where $n\neq1\operatorname{mod}(p-1)$, then $f=0$ is a consequence of multilinear Lie relators in fewer than $n$ variables. For years I have struggled to understand his proofs, and while I still have not the slightest clue about his proof in [J. Algebra 104 (1986), no. 1, 1--22], I finally have some understanding of his proof in [Lecture Notes in Mathematics, pp. 91--197, 1456, Springer-Verlag, Berlin, 1990]. In this note I offer my insights into Wall's second proof of this theorem.https://jims.ims.ir/article_107524_f75dbbf7321a14000589885d5d7b9665.pdf