# Strictly simple 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

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This article is about a standard (though not very rudimentary) definition in group theory. The article text may, however, contain more than just the basic definitionVIEW: Definitions built on this | Facts about this: (factscloselyrelated to Strictly simple group, all facts related to Strictly simple group) |Survey articles about this | Survey articles about definitions built on this

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## Definition

### Symbol-free definition

A group is said to be **strictly simple** if it has no proper nontrivial ascendant subgroup.

### In terms of the simple group operator

The group property of being absolutely simple is obtained by applying the simple group operator to the trim subgroup property of being an ascendant subgroup.