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oai:recercat.cat:2117/3906562026-01-22T04:05:08Zcom_2072_1033col_2072_452950

Inducing braces and Hopf Galois structures Crespo, Teresa Gil Muñoz, Daniel Río Doval, Ana Vela del Olmo, Maria Montserrat Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Anells i àlgebres Field theory (Physics) Left braces Holomorphs Regular subgroups Hopf Galois structures Teoria de camps (física) Classificació AMS::12 Field theory and polynomials::12F Field extensions © 2023 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Let p be a prime number and let n be an integer not divisible by p and such that every group of order np has a normal subgroup of order p. (This holds in particular for .) Under these hypotheses, we obtain a one-to-one correspondence between the isomorphism classes of braces of size np and the set of pairs , where runs over the isomorphism classes of braces of size n and runs over the classes of group morphisms from the multiplicative group of to ⁎ under a certain equivalence relation. This correspondence gives the classification of braces of size np from the one of braces of size n. From this result we derive a formula giving the number of Hopf Galois structures of abelian type on a Galois extension of degree np in terms of the number of Hopf Galois structures of abelian type E on a Galois extension of degree n. For a prime number , we apply the obtained results to describe all left braces of size 12p and determine the number of Hopf Galois structures of abelian type on a Galois extension of degree 12p. Peer Reviewed Postprint (published version) 2023-09-01 Article https://www.sciencedirect.com/science/article/pii/S0022404923000543 ©2023. Elsevier https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access Attribution-NonCommercial-NoDerivatives 4.0 International