Tactical decompositions in finite polar spaces and non-spreading classical group actions
arxiv(2024)
摘要
For finite classical groups acting naturally on the set of points of their
ambient polar spaces, the symmetry properties of synchronising and
separating are equivalent to natural and well-studied problems on the
existence of certain configurations in finite geometry. The more general class
of spreading permutation groups is harder to describe, and it is the
purpose of this paper to explore this property for finite classical groups. In
particular, we show that for most finite classical groups, their natural action
on the points of its polar space is non-spreading. We develop and use a result
on tactical decompositions (an AB-Lemma) that provides a useful
technique for finding witnesses for non-spreading permutation groups. We also
consider some of the other primitive actions of the classical groups.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要