Strictly 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
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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 definition
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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.

Relation with other properties

Stronger properties

Weaker properties