Normal implies modular
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., normal subgroup) must also satisfy the second group property (i.e., modular subgroup)
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Suppose is a normal subgroup of . Then, for any subgroup of and any subgroup of such that , we have:
- Normal implies permutable
- Permutable implies modular (which in turn uses modular property of groups)
The proof follows directly by combining facts (1) and (2).