SANOV’S THEOREM ON LIE RELATORS IN GROUPS OF EXPONENT p

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.