Metabelian implies subnormal join property

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This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., metabelian group) must also satisfy the second group property (i.e., group satisfying subnormal join property)
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A metabelian group satisfies the group satisfying subnormal join property: the join of any two Subnormal subgroup (?)s of the group is subnormal.

Facts used

  1. Metabelian implies nilpotent commutator subgroup
  2. Nilpotent commutator subgroup implies subnormal join property


The proof follows directly by combining facts (1) and (2).