@article {
author = {Vaughan-Lee, M.},
title = {Sanov's theorem on Lie relators in groups of exponent $p$},
journal = {Journal of the Iranian Mathematical Society},
volume = {2},
number = {1},
pages = {1-16},
year = {2021},
publisher = {Iranian Mathematical Society},
issn = {2717-1612},
eissn = {2717-1612},
doi = {10.30504/jims.2020.110856},
abstract = {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.},
keywords = {Sanov's theorem,Lie relators,Groups of exponent $p$},
url = {https://jims.ims.ir/article_110856.html},
eprint = {https://jims.ims.ir/article_110856_87c80830a05958c113d30d5f05f1c835.pdf}
}