The generalization of a theorem on real valued characters

Abstract: The Theorem of Ito-Michler, one of the most celebrated results in character theory of finite groups, states that a group has a normal abelian Sylow $p$-subgroup if and only if the prime number $p$ does not divide the degree of any irreducible character of the group.

Among the many variants of the theorem, there exists one, due to Dolfi, Navarro and Tiep, which involves only the real valued irreducible characters of the group, and the prime number $p = 2$.

This variant, however, fails if we consider a prime number different from 2, and any generalization in this direction seems hard, due to some specific properties of real valued characters.

This talk proposes a new way to approach the problem, which takes into account a different subset of the irreducible characters, however related with real valued characters. This new approach has already been partially successful and it may suggest a way to generalize also other similar results.

group theory

Audience: researchers in the topic

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Finite Groups in Valencia

Series comments: The seminar meets weekly from February 26th to March 30th 2021.

For a detailed schedule and registration details, please visit the seminar webpage at

sites.google.com/view/finite-groups-seminar2021

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