Noether's problem for orientation $p$-subgroups of symmetric groups

TL;DR

This paper solves Noether's rationality problem for specific index p subgroups of p-Sylow subgroups within symmetric groups, advancing understanding of group actions on rational function fields.

Contribution

It provides a positive solution to Noether's problem for certain orientation p-subgroups of symmetric groups, a case previously unresolved.

Findings

Confirmed rationality for specific p-subgroups

Extended the class of groups known to satisfy Noether's problem

Enhanced understanding of group actions on rational fields

Abstract

We give a positive solution to Noether's rationality problem for certain index $p$ subgroups of the $p$-Sylow subgoups of symmetric groups.