TY - JOUR
ID - 107524
TI - Understanding Wall's theorem on dependence of Lie relators in Burnside groups
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 - 2020
PY - 2020
VL - 1
IS - 2
SP - 129
EP - 143
KW - Lie relators
KW - Burnside groups
KW - Wall's theorem
DO - 10.30504/jims.2020.107524
N2 - G.E. Wall [J. Algebra 104 (1986), no. 1, 1--22; Lecture Notes in Mathematics, pp. 191--197, 1456, Springer-Verlag, Berlin, 1990] gave two different proofs of a remarkable result about the multilinear Lie relators satisfied by groups of prime power exponent $q$. He showed that if $q$ is a power of the prime $p$, and if $f$ is a multilinear Lie relator in $n$ variables where $n\neq1\operatorname{mod}(p-1)$, then $f=0$ is a consequence of multilinear Lie relators in fewer than $n$ variables. For years I have struggled to understand his proofs, and while I still have not the slightest clue about his proof in [J. Algebra 104 (1986), no. 1, 1--22], I finally have some understanding of his proof in [Lecture Notes in Mathematics, pp. 91--197, 1456, Springer-Verlag, Berlin, 1990]. In this note I offer my insights into Wall's second proof of this theorem.
UR - https://jims.ims.ir/article_107524.html
L1 - https://jims.ims.ir/article_107524_f75dbbf7321a14000589885d5d7b9665.pdf
ER -