For a group of order , where is a prime with , we consider the regular subgroups that are normalized by , the left regular representation of . These subgroups are in one-to-one correspondence with the Hopf–Galois structures on separable field extensions with . Elsewhere we showed that if then all such lie within the normalizer of the Sylow -subgroup of . Here we show that one only need assume that all groups of a given order have a unique Sylow -subgroup, and that not be a divisor of the order of the automorphism groups of any group of order . We thus extend the applicability of the program for computing these regular subgroups and concordantly the corresponding Hopf–Galois structures on separable extensions of degree .
"Hopf–Galois structures arising from groups with unique subgroup of order $p$." Algebra Number Theory 10 (1) 37 - 59, 2016. https://doi.org/10.2140/ant.2016.10.37