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- W2342260813 abstract "Let L/K be a Galois extension of fields with Galois group G an elementary abelian p-group of rank n for p an odd prime. It is known that nilpotent ring structures A on G yield regular subgroups of the holomorph Hol(G), and in turn Hopf Galois structures on L/K. In this paper we describe these structures in two cases. If A^3 = 0 the corresponding regular subgroup yields Hopf Galois structures directly, without translating from Hol(G) to Perm(G). We determine the number of Hopf Galois structures that arise when dim(A^2) = 1, which yields a new lower bound on the number of Hopf Galois structures on L/K when $n = 4. We also look at the case when dim(A/A^2) = 1." @default.
- W2342260813 created "2016-06-24" @default.
- W2342260813 creator A5006862487 @default.
- W2342260813 date "2016-04-18" @default.
- W2342260813 modified "2023-09-27" @default.
- W2342260813 title "Obtaining abelian Hopf Galois structures from finite commutative nilpotent rings" @default.
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