%0 Journal Article
%T Sanov's theorem on Lie relators in groups of exponent $p$
%J Journal of the Iranian Mathematical Society
%I Iranian Mathematical Society
%Z 2717-1612
%A Vaughan-Lee, M.
%D 2021
%\ 01/01/2021
%V 2
%N 1
%P 1-16
%! Sanov's theorem on Lie relators in groups of exponent $p$
%K Sanov's theorem
%K Lie relators
%K Groups of exponent $p$
%R 10.30504/jims.2020.110856
%X 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.
%U https://jims.ims.ir/article_110856_87c80830a05958c113d30d5f05f1c835.pdf