Class 2 quotients of solvable linear groups

Thomas Keller; Yong Yang

Class 2 quotients of solvable linear groups

Group Theory 2017-10-06 v1

Authors: Thomas Keller , Yong Yang

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 $|V|$ .

Keywords

finite group theory nilpotent groups representation theory of groups

Cite

@article{arxiv.1710.01860,
  title  = {Class 2 quotients of solvable linear groups},
  author = {Thomas Keller and Yong Yang},
  journal= {arXiv preprint arXiv:1710.01860},
  year   = {2017}
}

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