科研之友
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摘要
Let G be a finite group, and let V be a completely reducible faithful G-module. It has been known for a long time that if G is abelian, then G has a regular orbit on V. In this paper we generalize this result as follows. Assuming G to be solvable, we show that G has an orbit of size at least vertical bar G/G'vertical bar on V. This also strengthens a result of Aschbacher and Guralnick in that situation. Additionally, we prove a similar generalization of the well-known result that if G is nilpotent, then G has an orbit of size at least root vertical bar G vertical bar on V.
- 出版日期2016-2
