BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicola Grittini (University of Florence) DTSTART:20201203T143000Z DTEND:20201203T153000Z DTSTAMP:20260423T024613Z UID:AlBicocca/7 DESCRIPTION:Title: Problems on character theory when we restrict the field of values\nb y Nicola Grittini (University of Florence) as part of Al@Bicocca take-away \n\n\nAbstract\nIrreducible characters of rational and real values have al ways attracted the attention of researchers in Character theory of finite groups. One of the questions which naturally arise when these characters a re studied\, among the others\, is whether some of the most famous results in character theory have variants involving rational or real valued chara cters. In fact\, some of these results have such variants and\, maybe not surprisingly\, the variants often involve the prime number 2. An example o f this fact is a theorem proved in 2007 by Dolfi\, Navarro and Tiep. The t heorem is a real-valued version of Ito-Michler Theorem and says that\, if no real-valued irreducible character of a finite group $G$ has even order\ , then the group has a normal Sylow 2-subgroup.\n\nOn the other hand\, it is quite difficult to work with rational and real valued characters if we consider a prime number different from 2. This suggests that\, if we want to find variants of some classical results involving character fields of v alues and an odd prime number $p$\, we may not consider as fields $\\mathb b{Q}$ and $\\mathbb{R}$ but some other fields\, whose definition involves the prime $p$ and which are equal to $\\mathbb{Q}$ or $\\mathbb{R}$ when $ p= 2$. \n\nIn this talk we will see two cases in which this generalization is possible\,one involving rational valued and one involving real valued characters. The part involving real-valued characters has been published i n a preprint and has to be considered as a work in progress\, nevertheless the approach followed in the study of the problem could be interesting fo r many researchers in character theory.\n LOCATION:https://researchseminars.org/talk/AlBicocca/7/ END:VEVENT END:VCALENDAR