Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 2 1 2021 01 01 Sanov's theorem on Lie relators in groups of exponent $p$ 1 16 110856 10.30504/jims.2020.110856 EN M. Vaughan-Lee Christ Church, University of Oxford, Oxford, OX1 1DP, England. Journal Article 2020 05 15 ‎I 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. https://jims.ims.ir/article_110856_687456d6fc92f14de8f8c4acc7716e6f.pdf