# Fitting-free group

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

This is a variation of simplicity|Find other variations of simplicity | Read a survey article on varying simplicity

## Contents

## Definition

### Symbol-free definition

A subgroup of a group is said to be **Fitting-free** if it satisfies the following equivalent conditions:

- It has no nontrivial nilpotent normal subgroup
- Its Fitting subgroup is trivial