Normality-preserving endomorphism-invariant implies finite direct power-closed characteristic
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., normality-preserving endomorphism-invariant subgroup) must also satisfy the second subgroup property (i.e., finite direct power-closed characteristic subgroup)
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- Normality-preserving endomorphism-invariance is finite direct power-closed
- Normality-preserving endomorphism-invariant implies characteristic
The proof follows by combining facts (1) and (2).