Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16121320200901Sanov's theorem on Lie relators in groups of exponent $p$17318811085610.30504/jims.2020.110856ENM.Vaughan-LeeChrist Church, University of Oxford,
Oxford, OX1 1DP, England.Journal Article20200515I give a proof of Sanov's theorem that the Lie relators of weight at most $2p-2$ in groups of exponent $p$ are consequences of the identity $px=0$ and the $(p-1)$-Engel identity. This implies that the order of the class $2p-2$ quotient of the Burnside group $B(m,p)$ is the same as the order of the class $2p-2$ quotient of the free $m$ generator $(p-1)$-Engel Lie algebra over GF$(p)$. To make the proof self-contained I have also included a derivation of Hausdorff's formulation of the Baker Campbell Hausdorff formula.http://jims.ims.ir/article_110856_d74d515fe59b31df18d4dd5e51336858.pdf