Marginal implies 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., marginal subgroup) must also satisfy the second subgroup property (i.e., direct power-closed characteristic subgroup)
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Suppose is a group and is a marginal subgroup of , i.e., there is a collection of words such that is precisely the set of elements of by which left or right multiplication on any letter of the word does not affect the value of the word.
- Center is direct power-closed characteristic: Follows by combining this fact with center is marginal.
The proof follows immediately from facts (1) and (2).