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Enumerating Dihedral Hopf-Galois Structures Acting on Dihedral Extensions | | Timothy Kohl
; | | Date: |
8 Jul 2019 | | Abstract: | The work of Greither and Pareigis details the enumeration of the Hopf-Galois
structures (if any) on a given separable field extension. For an extension
$L/K$ which is classically Galois with $G=Gal(L/K)$ the Hopf algebras in
question are of the form $(L[N])^{G}$ where $Nleq B=Perm(G)$ is a regular
subgroup that is normalized by the left regular representation $lambda(G)leq
B$. We consider the case where both $G$ and $N$ are isomorphic to a dihedral
group $D_n$ for any $ngeq 3$. Using the normal block systems inherent to the
left regular representation of each $D_n$,(and every other regular permutation
group isomorphic to $D_n$) we explicitly enumerate all possible such $N$ which
arise. | | Source: | arXiv, 1907.3844 | | Services: | Forum | Review | PDF | Favorites | |
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