Admissible groups over two dimensional complete local domains

TL;DR

This paper characterizes when a finite group is admissible over a two-dimensional complete local domain with a separably closed residue field, linking admissibility to the abelian nature and rank of Sylow subgroups.

Contribution

It provides a complete criterion for admissibility of finite groups over such domains based on Sylow subgroup structure, extending understanding in algebraic geometry and number theory.

Findings

G is admissible over K iff Sylow subgroups are abelian of rank ≤ 2

Characterization applies to domains with separably closed residue fields

Advances the classification of finite groups over local domains

Abstract

Let K be the quotient field of a complete local domain of dimension 2 with a separably closed residue field. Let G be a finite group of order not divisible by char(K). Then G is admissible over K if and only if its Sylow subgroups are abelian of rank at most 2.