Every coprime linear group admits a base of size two
Every coprime linear group admits a base of size two
复制标题
DOI：
10.1090/tran/6544
复制
发表时间：
2012-12
影响因子：
1.3
通讯作者：
Z. Halasi;K. Podoski
中科院分区：
文献类型：
--
作者：
Z. Halasi;K. Podoski
设G是作用在有限向量空间V上的线性群，并假设（|G|,|V|）=1.在本文中，我们证明了G有一个基大小最多为2，这个估计是尖锐的。这推广和加强了以前关于互素线性群的基大小的几个结果。作为一个直接的结果，我们回答了一个问题。M.艾萨克斯同意通过大轨道，这与k（GV）定理有关。
Let G be a linear group acting on the finite vector space V and assume that (|G|,|V|)=1. In this paper we prove that G has a base size at most two and this estimate is sharp. This generalizes and strengthens several former results concerning base sizes of coprime linear groups. As a direct consequence, we answer a question of I. M. Isaacs in the affirmative. Via large orbits this is related to the k(GV) theorem.