In mathematics, in the field of group theory, a group is said to be characteristically simple if it has no proper nontrivial characteristic subgroups.
Characteristically simple is a weaker condition than being a simple group, as simple groups must not have any proper nontrivial normal subgroups, which include characteristic subgroups.
A finite group is characteristically simple if and only if it is a direct product of isomorphic simple groups.
Every minimal normal subgroup of a group is characteristically simple.
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