# 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.[1] That is, ${\displaystyle G}$ is an absolutely simple group if the only serial subgroups of ${\displaystyle G}$ are ${\displaystyle \{e\}}$ (the trivial subgroup), and ${\displaystyle G}$ itself (the whole group).