Strictly simple group

In mathematics, in the field of group theory, a group is said to be strictly simple if it has no proper nontrivial ascendant subgroups. That is, formula_1 is a strictly simple group if the only ascendant subgroups of formula_1 are formula_3 (the trivial subgroup), and formula_1 itself (the whole group).
In the finite case, a group is strictly simple if and only if it is simple. However, in the infinite case, strictly simple is a stronger property than simple.
References.
Simple Group Encyclopedia of Mathematics, retrieved 1 January 2012