Orbits and Stabilizers for Solvable Linear Groups
Printed: Jun 2006
We extend a result of Noritzsch,
which describes the orbit sizes in the action of a
Frobenius group $G$ on a finite vector space $V$ under
certain conditions, to a more general class of finite
solvable groups $G$.
This result has applications in computing
irreducible character degrees of finite groups.
Another application, proved here, is a result
concerning the structure of certain groups with
few complex irreducible character degrees.
20B99 - None of the above, but in this section
20C15 - Ordinary representations and characters
20C20 - Modular representations and characters