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Abelian Quotients and Orbit Sizes of Finite Groups by Keller, Thomas Michael; Yang, Yong is a scholarly article available to read on EtoBox.

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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 show that $G$ has an orbit of size at least $|G/G'|$ on $V$. This generalizes earlier work of the authors, where the same bound was proved under the additional hypothesis that $G$ is solvable. For completely reducible modules it also strengthens the 1989 result $|G/G'|<|V|$ by Aschbacher and Guralnick.

Author

Keller, Thomas Michael; Yang, Yong

Published

2014

Language

EN