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, ${\displaystyle G}$ is a strictly simple group if the only ascendant subgroups of ${\displaystyle G}$ are ${\displaystyle \{e\}}$ (the trivial subgroup), and ${\displaystyle G}$ 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.