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## Homework Statement

If J is a subgroup of G whose order is a power of a pirme p, prove that J must be contained in a Sylow p-subgroup of G.

(Take H to be a Sylow p-subgroup of G and let X be the set of left cosets of H. Define an action of G on X by g(xH) = gxH and consider the induced action of J on X)

## Homework Equations

## The Attempt at a Solution

I am not sure how to begin on this one and I am also unclear on how the hint involving the group action helps in this proof.