AI 中文总结
研究任意域上射影线性群有限子群及特定多项式相关有限子群的可提升性，通过结合群上同调的限制与上限制及归约到克莱因方法，建立了可提升性的西罗准则。
AI 中文摘要
本文首先建立了任意域上射影线性群有限子群可提升性的西罗准则。还得到了\(F -\)可提升性的西罗准则：若\(F\)是特征零域上\(N\)个变量的\(d\)次非奇异多项式，\(\mathrm{Lin}(F)\)的有限子群\(G\)是\(F -\)可提升的，当且仅当对整除\(\gcd(|G|,N,d)\)的每个素数\(p\)，\(G\)存在一个\(F -\)可提升的西罗\(p -\)子群。证明结合了群上同调中的限制与上限制以及归约到克莱因方法。
英文摘要
In this paper, we first establish Sylow criteria for liftability of finite subgroups of the projective linear groups over arbitrary field. We also obtain Sylow criteria for $F$-liftability: if $F$ is a nonsingular polynomial of degree $d$ in $N$ variables over a field of characteristic zero, then a finite subgroup $G$ of $\mathrm{Lin}(F)$ is $F$-liftable if and only if for every prime $p$ dividing $\gcd(|G|,N,d)$, there exists a Sylow $p$-subgroup of $G$ that is $F$-liftable. Our proof combines restriction and corestriction in group cohomology with the reduction-to-Klein method.
Comments15 pages. Comments welcome!
