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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… Click to show full 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:
linear groups;
class;
class quotients;
solvable linear;
quotients solvable
Journal Title: Journal of Algebra
Year Published: 2018
Link to full text (if available)
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Journal Title: Journal of Algebra
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!