Über die Grade irreduzibler Charaktere endlicher Gruppen (Q1061834)

The author proves several results on the degrees of irreducible characters of finite groups. There are two main results. 1. Let G be a finite non-p-nilpotent (non-p-solvable) group and let \(\{\chi_ 1,...,\chi_ t\}\subseteq Irr G\) for which \(G/Ker(\chi_ i)\) is not p- nilpotent (not p-solvable) and for which \(p\nmid \chi_ i(1)\) \((i=1,...,t)\). Then \(\sum^{t}_{i=1}\chi_ i(1)\geq p-1\). 2. Let G be a 2-fold transitive permutation group of degree n, H the stabilizer of a point, p a prime with \(p\nmid n\). Then \(G/O^ p(G)\cong H/O^ p(H)\) or there is a linear character \(\lambda\) of H, with \(\lambda^ G\) irreducible and \(G/Ker(\lambda^ G)\) is not p-nilpotent.