Integral group rings with all central units trivial: solvable groups

TL;DR

This paper investigates finite solvable groups whose integral group rings have only trivial central units, aiming to classify and understand the structure of such groups.

Contribution

It provides a classification of finite solvable groups with integral group rings having only trivial central units, advancing understanding in group ring theory.

Findings

Characterization of solvable groups with trivial central units

Identification of structural properties leading to trivial central units

Extension of previous results to a broader class of groups

Abstract

The object of this paper is to examine finite solvable groups whose integral group rings have only trivial central units.