Skew braces and Hopf-Galois structures of Heisenberg type

摘要

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 p(3). Crown Copyright (C) 2019 Published by Elsevier Inc. All rights reserved.