Inducing braces and Hopf Galois structures

Let p be a prime number and let n an integer not divisible by such that every group of order np has normal subgroup p. (This holds in particular for p>n.) Under these hypotheses, we obtain one-to-one correspondence between the isomorphism classes braces size set pairs (Bn,[τ]), where Bn runs over [τ] morphisms from multiplicative to Zp⁎ under certain equivalence relation. This gives classification one n. From this result derive formula giving Hopf Galois structures abelian type Zp×E on extension degree terms E For p≥7, apply obtained results describe all left 12p determine 12p.