# 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).