# Core-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 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.VIEW: Definitions built on this | Facts about this: (factscloselyrelated to Core-free group, all facts related to Core-free group) |Survey articles about this | Survey articles about definitions built on this

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View a list of other standard non-basic definitions

## Definition

### Symbol-free definition

A finite group is said to be **core-free** if it satisfies the following conditions:

- It has no nontrivial normal subgroup of odd order
- The Brauer core is trivial

## Relation with other properties

### Stronger properties

- non-Abelian simple group
- semisimple group