# Absolutely 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

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

## Definition

### Symbol-free definition

A group is said to be **absolutely simple** if it has no proper nontrivial serial 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 a serial subgroup.