Class 2 quotients of solvable linear groups
Thomas Keller, Yong Yang

TL;DR
This paper generalizes a known bound on the order of nilpotent class 2 groups acting on modules, extending it to solvable groups and their maximal class 2 quotients, showing they are strictly bounded by the module size.
Contribution
It proves that for solvable groups, the order of the maximal class 2 quotient is strictly less than the size of a faithful, completely reducible module.
Findings
Maximal class 2 quotient order is strictly less than module size
Generalizes Glauberman's result from nilpotent to solvable groups
Provides bounds on group quotients in relation to module dimensions
Abstract
Let be a finite group, and let be a completely reducible faithful -module. By a result of Glauberman it has been known for a long time that if is nilpotent of class 2, then . In this paper we generalize this result as follows. Assuming to be solvable, we show that the order of the maximal class 2 quotient of is strictly bounded above by .
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems
