Absolutely simple group

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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
View a complete list of group properties
VIEW 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


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.