Fitting-free group

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This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.
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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Symbol-free definition

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

Equivalence of definitions

The key idea is to use the fact that any nontrivial solvable group has a nontrivial Abelian characteristic subgroup. Template:FurtheR

Relation with other properties

Stronger properties

Weaker properties