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Hopf Galois structures, skew braces for groups of size $p^nq$: The cyclic Sylow subgroup case (2309.06848v1)
Published 13 Sep 2023 in math.GR and math.RA
Abstract: Let $n\geq 1$ be an integer, $p$, $q$ be distinct odd primes. Let ${G}$, $N$ be two groups of order $pnq$ with their Sylow-$p$-subgroups being cyclic. We enumerate the Hopf-Galois structures on a Galois ${G}$-extension, with type $N$. This also computes the number of skew braces with additive group isomorphic to $G$ and multiplicative group isomorphic to $N$. Further when $q<p$, we give a complete classification of the Hopf-Galois structures on Galois-$G$-extensions.