Class 2 quotients of solvable linear groups

Thomas Keller; Yong Yang

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arXiv · 1710.01860

Class 2 quotients of solvable linear groups

Thomas Keller·Yong Yang

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Abstract

Let $G$ be a finite group, and let $V$ be a completely reducible faithful $G$-module. By a result of Glauberman it has been known for a long time that if $G$ is nilpotent of class 2, then $|G| < |V|$. In this paper we generalize this result as follows. Assuming $G$ to be solvable, we show that the order of the maximal class 2 quotient of $G$ is strictly bounded above by $|V|$.

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Thomas Keller, Yong Yang. 2017-10-05. Class 2 quotients of solvable linear groups. https://arxiv.org/abs/1710.01860

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