Absolutely simple group

In mathematics, in the field of group theory, a group is said to be absolutely simple if it has no proper nontrivial serial subgroups. That is, formula_1 is an absolutely simple group if the only serial subgroups of formula_1 are formula_3 (the trivial subgroup), and formula_1 itself (the whole group).
In the finite case, a group is absolutely simple if and only if it is simple. However, in the infinite case, absolutely simple is a stronger property than simple. The property of being strictly simple is somewhere in between.