Seminario Teoría de Grupos
POSPUESTO - On groups with quadratic rational character values - POSTPONED
Ponente: Ángel del Río (Universidad de Murcia)Fecha: jueves 16 de enero de 2025 - 11:00Lugar: Aula Naranja, ICMAT
Resumen:
A finite group is said to be rational or rationally valued if its character table is formed by rational numbers. Although rationality is a strong condition, their study is a classical topic in character theory because some relevant groups, as for example the symmetric groups, are rational.
During the last years several authors have considered groups for which each character value belongs to a quadratic extension of the rationals.
These have led to several classes of groups depending on whether it is required that the full character table is contained in a fixed quadratic extension of the rational, or this condition is required per rows or columns of the character table. The groups satisfying the condition per rows are known as quadratic rational groups and those satisfying the conditions per columns are called semi-rational.
In this talk we discuss relations between some of these conditions with special emphasis on uniformly semi-rational groups which are groups G satisfying the following conditions for some integer r relatively prime with the exponent of G: For every g in G, every generator of the cyclic group generated by g is conjugate in G to g or g^r.
Joint work with Marco Vergani.
