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, is an absolutely simple group if the only serial subgroups of are (the trivial subgroup), and 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. See also Ascendant subgroup Strictly simple group References Properties of groups