2026-04-17T20:35:05Zhttps://recercat.cat/oai/request

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 Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. STNB - Seminari de Teoria de Nombres de Barcelona 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 Crespo, T. [et al.]. Inducing braces and Hopf Galois structures. "Journal of pure and applied algebra", 1 Setembre 2023, vol. 227, núm. article 107371. 0022-4049 https://hdl.handle.net/2117/390656 10.1016/j.jpaa.2023.107371 eng 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 application/pdf