# Hall implies order-dominating in finite solvable

From Groupprops

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a finite solvable group. That is, it states that in a Finite solvable group (?), every subgroup satisfying the first subgroup property (i.e., Hall subgroup (?)) must also satisfy the second subgroup property (i.e., Order-dominating subgroup (?)). In other words, every Hall subgroup of finite solvable group is a order-dominating subgroup of finite solvable group.

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## Statement

In a finite solvable group, every Hall subgroup is order-dominating.