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Kernels of minimal characters of solvable groups
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- Journal:
- Proceedings of the Edinburgh Mathematical Society , First View
- Published online by Cambridge University Press:
- 06 November 2024, pp. 1-4
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Let G be a finite solvable group. We prove that if
$\chi\in{{\operatorname{Irr}}}(G)$ has odd degree and 
$\chi(1)$ is the minimal degree of the nonlinear irreducible characters of G, then 
$G/\operatorname{Ker}\chi$ is nilpotent-by-abelian.
