On the Galois embedding problem associated to the universal central extension of the alternating group of degree 6

© 2013. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We obtain an explicit expression for the obstruction to the solvability of the Galois embedding problem associated to the universal central extension of the alternating group of degree 6.Peer ReviewedPostprint (author's final draft

Hopf Galois structures on symmetric and alternating extensions

By using a recent theorem by Koch, Kohl, Truman and Underwood on normality, we determine that some types of Hopf Galois structures do not occur on Galois extensions with Galois group isomorphic to alternating or symmetric groups. Our theory of induced Hopf Galois structures allows us to obtain the whole picture of types of Hopf Galois structures on A4-extensions, S4-extensions, and S5-extensions. Combining it with a result of Carnahan and Childs, we obtain a complete count of the Hopf Galois structures on S5-extensions.Peer ReviewedPostprint (author's final draft

Inducing braces and Hopf Galois structures

© 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 ReviewedPostprint (published version

Left braces of size 8 p

We describe all left braces aof size 8 p for an odd p diferent from 3 and 7.Postprint (author's final draft

On the Galois correspondence theorem in separable Hopf Galois theory

In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis. We prove that the class of Hopf Galois extensions for which the Galois correspondence is bijective is larger than the class of almost classically Galois extensions but not equal to the whole class. We show as well that the image of the Galois correspondence does not determine the Hopf Galois structure.Peer ReviewedPostprint (author's final draft

A UPC innovation teaching project for the incorporation of the gender perspective in nautical, marine and naval engineering

There has been a rising awareness in recent years of the gender inequalities within STEM-related programmes and the need to overcome them and so bridge the gender gap in these academic disciplines. Different initiatives have arisen, among which there are gender equality policies, regulations and programmes. In line with this, the Catalan University Quality Assurance Agency (AQU) promoted a regulation for the incorporation of the gender perspective in all the bachelor’s and master’s degrees in tertiary education in Catalonia by 2021. To comply with this regulation and also to promote a culture of equity and equality of opportunities for women, the Universitat Politècnica de Catalunya (UPC) fostered different projects within its community. One of these projects has been developed by the Gender Equality Commission at Barcelona School of Nautical Studies and consists in the development of a web platform with resources for lecturers to incorporate this new transversal competence of gender perspective in the nautical, marine and naval engineering study plans. The main objective of this teaching innovation project is to aid teachers with the incorporation of this competence not only by providing online tools and resources but also gender-focused teacher training to allow them to design tailor-made activities and strategies. Some tests were also administered to assess the effectiveness of the implementation of these newly-designed gender equality teaching practices and some sample study plans and activities were developed to serve as a model and example of good practices for the incorporation of gender mainstreaming in the disciplines of nautical, marine and naval engineering

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