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Finite solvable groups with a rational skew-field of noncommutative real rational invariants
Podlogar, Gregor, matematik
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 ▫$5$▫.
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