Strictly simple group

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.

Stronger properties

 * Absolutely simple group

Weaker properties

 * Simple group
 * Characteristically simple group