On p-embedding problems in characteristic p

TL;DR

This paper proves that in characteristic p>0, finite embedding problems with p-group kernels over valued fields with non-p-divisible value groups are always properly solvable, advancing understanding in field theory.

Contribution

It establishes proper solvability of p-group embedding problems in valued fields of characteristic p with non-p-divisible value groups, a new result in field theory.

Findings

Finite embedding problems with p-group kernels are properly solvable in the specified fields.

The result applies specifically to valued fields of characteristic p with non-p-divisible value groups.

Abstract

Let K be a valued field of characteristic p>0 with non-p-divisible value group. We show that every finite embedding problem for K whose kernel is a p-group is properly solvable.