Abstract: We consider Noether’s problem on the noncommutative rational functions invariant under a linear action of a finite group. For abelian groups the invariant skew-fields are always rational, for solvable group they are rational if the action is well-behaved – given by a so-called complete representation. We determine the groups that admit such representations and call them totally pseudo-unramified. We show that for a solvable group the invariant skew-field is finitely generated. Finally we study totally pseudo-unramified groups and classify totally pseudo-unramified ▫$p$▫-groups of rank at most ▫$5$▫.Keywords: Clifford theory, multiplicity free restrictions, noncommutative Noether’s problem, noncommutative rational invariant, totally unramified groupsPublished in DiRROS: 03.07.2024; Views: 18; Downloads: 18 Full text (2,18 MB)This document has many files! More...
