| Abstract: |
| On character degrees of a finite group $G$, the well-known Thompson theorem states that if a prime $p$ divides the degree of every nonlinear irreducible character of $G$, then $G$ has a normal $p$-complement, and the Ito-Michler theorem states that if $p$ does not divide the degree of every irreducible character of $G$, then $G$ has a normal Sylow $p$-subgroup. In this talk, we give the strengthened versions of Thompson theorem and Ito-Michler theorem in terms of the sum of all ordinary irreducible characters of $G$ of degree coprime $p$ or divisible by $p$. |
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