Endomorph-dominating not implies automorph-conjugate
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., endomorph-dominating subgroup) need not satisfy the second subgroup property (i.e., automorph-conjugate subgroup)
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- is an endomorph-dominating subgroup of : For every endomorphism of , there exists such that .
- is not an automorph-conjugate subgroup of : There exists an automorphism of such that and are not conjugate subgroups.
We take and as a copy of inside the base .