dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Universitat Politècnica de Catalunya. STNB - Seminari de Teoria de Nombres de Barcelona
dc.contributor.author
Crespo, Teresa
dc.contributor.author
Gil Muñoz, Daniel
dc.contributor.author
Río Doval, Ana
dc.contributor.author
Vela del Olmo, Maria Montserrat
dc.date.issued
2023-09-01
dc.identifier
Crespo, T. [et al.]. Inducing braces and Hopf Galois structures. "Journal of pure and applied algebra", 1 Setembre 2023, vol. 227, núm. article 107371.
dc.identifier
https://hdl.handle.net/2117/390656
dc.identifier
10.1016/j.jpaa.2023.107371
dc.description.abstract
© 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/
dc.description.abstract
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.
dc.description.abstract
Peer Reviewed
dc.description.abstract
Postprint (published version)
dc.format
application/pdf
dc.relation
https://www.sciencedirect.com/science/article/pii/S0022404923000543
dc.rights
©2023. Elsevier
dc.rights
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights
Attribution-NonCommercial-NoDerivatives 4.0 International
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Anells i àlgebres
dc.subject
Field theory (Physics)
dc.subject
Regular subgroups
dc.subject
Hopf Galois structures
dc.subject
Teoria de camps (física)
dc.subject
Classificació AMS::12 Field theory and polynomials::12F Field extensions
dc.title
Inducing braces and Hopf Galois structures
