半线性群元素的Desarguesian展开和域约化
Desarguesian spreads and field reduction for elements of the semilinear group
摘要：
本文的目的是为有限射影空间的域归约、作用于定义向量空间的一般半线性群和射影半线性群之间的相互作用建立一个合理的框架。这一方法使得Dye关于Desklesian价差的PGL中稳定子的一个结果有可能以更初等的方式得到重新证明，并将其推广到PΓL（n，q）.此外，Drudge [5]将Singer循环与Despermesian传播联系起来的结果，以及关于子传播的结果（由Sheekey，Rottey和Van de Voorde [19]），以类似的基本方式重新证明。最后，我们尝试使用这种方法来阐明Csajbok和Zanella在线性集研究中引入的条件（A）[4]。
英文摘要：
The goal of this note is to create a sound framework for the interplay between field reduction for finite projective spaces, the general semilinear groups acting on the defining vector spaces and the projective semilinear groups. This approach makes it possible to reprove a result of Dye on the stabiliser in PGL of a Desarguesian spread in a more elementary way, and extend it to PΓL(n, q). Moreover a result of Drudge [5] relating Singer cycles with Desarguesian spreads, as well as a result on subspreads (by Sheekey, Rottey and Van de Voorde [19]) are reproven in a similar elementary way. Finally, we try to use this approach to shed a light on Condition (A) of Csajbok and Zanella, introduced in the study of linear sets [4].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
