simple group Simple 2002-02-19 11:36:00 2007-01-25 05:38:34 Definition simple A non-trivial group $G$ is said to be \emph{simple} if the only normal subgroups of $G$ are $\{1\}$ and $G$ itself. Equivalently, a simple group is a group in which the trivial subgroup is a maximal normal subgroup.