Skew Braces and Hopf-Galois Structures of Heisenberg Type
Abstract
We classify all skew braces of Heisenberg type for a prime number p>3 . Furthermore, we determine the automorphism group of each one of these skew braces (as well as their socle and annihilator). Hence, by utilising a link between skew braces and Hopf-Galois theory, we can determine all Hopf-Galois structures of Heisenberg type on Galois field extensions of fields of degree p3 .
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