Sanov's theorem on Lie relators in groups of exponent $p$

Document Type : Research Article


Christ Church, University of Oxford, Oxford, OX1 1DP, England.


‎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.


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