TY - JOUR
ID - 110856
TI - Sanov's theorem on Lie relators in groups of exponent $p$
JO - Journal of the Iranian Mathematical Society
JA - JIMS
LA - en
SN -
AU - Vaughan-Lee, M.
AD - Christ Church, University of Oxford,
Oxford, OX1 1DP, England.
Y1 - 2021
PY - 2021
VL - 2
IS - 1
SP - 1
EP - 16
KW - Sanov's theorem
KW - Lie relators
KW - Groups of exponent $p$
DO - 10.30504/jims.2020.110856
N2 - 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.
UR - https://jims.ims.ir/article_110856.html
L1 - https://jims.ims.ir/article_110856_87c80830a05958c113d30d5f05f1c835.pdf
ER -