Quelques r\'eflexions in\'evitables (Some inevitable considerations)

TL;DR

This paper extends Frécon's concept of the inevitable radical from groups in simple theories to those in stable and more general theories, broadening its applicability.

Contribution

It introduces a generalized construction of the inevitable radical applicable to groups in stable and simple theories, expanding the theoretical framework.

Findings

Generalization of Frécon's radical to stable theories

Application to groups in simple theories

Broader understanding of group structure in model theory

Abstract

We generalize Fr\'econ's construction of the inevitable radical to groups in stable and even simple theories.