On semiabelian p-groups

TL;DR

This paper proves that the family of semiabelian p-groups is fully characterized by a specific subfamily, thereby completing the solution to the minimal ramification problem for all semiabelian p-groups.

Contribution

The paper demonstrates that the subfamily G_p encompasses all semiabelian p-groups, extending previous results to the entire family.

Findings

G_p equals the entire family of semiabelian p-groups

Complete solution to the minimal ramification problem for semiabelian p-groups

Unified understanding of semiabelian p-groups structure

Abstract

The family of semiabelian p-groups is the minimal family that contains {1} and is closed under quotients and semidirect products with finite abelian p-groups. Kisilevsky and Sonn have solved the minimal ramification problem for a certain subfamily G_p of the family of semiabelian p-groups. We show that G_p is in fact the entire family of semiabelian p-groups and by this complete their solution to all semiabelian p-groups.