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, is a strictly simple group if the only ascendant subgroups of are (the trivial subgroup), and 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. See also Serial subgroup Absolutely simple group References Simple Group Encyclopedia of Mathematics, retrieved 1 January 2012 Properties of groups