Characteristic not implies direct factor
This article gives the statement and possibly, proof, of a non-implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., characteristic subgroup) need not satisfy the second subgroup property (i.e., direct factor)
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- is a normal subgroup of .
- is not a direct factor of : In fact, it is the only proper nontrivial subgroup of .