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is the trivial subgroup. Every minimal normal subgroup of a group is characteristically simple. This follows from the fact that a characteristic subgroup of a normal subgroup is normal.
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form a characteristically simple group that is not a direct product of simple groups.
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A finite group is characteristically simple if and only if it is a
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is characteristically simple if and only if it is an
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40:. Characteristically simple is a
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