Inducing braces and Hopf Galois structures

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472015" target="_blank" >RIV/00216208:11320/23:10472015 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Ja2Kal-fM0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Ja2Kal-fM0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jpaa.2023.107371" target="_blank" >10.1016/j.jpaa.2023.107371</a>

Result language
angličtina
Original language name
Inducing braces and Hopf Galois structures
Original language description
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 p > n.) Under these hypotheses, we obtain a one-to-one correspondence between the isomorphism classes of braces of size np and the set of pairs (B-n, [t]), where Bn runs over the isomorphism classes of braces of size n and [t] runs over the classes of group morphisms from the multiplicative group of B-n to Z*(p) 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 Z(p) x E 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 p >= 7, 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. (c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons .org /licenses /by -nc -nd /4 .0/).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GM21-00420M" target="_blank" >GM21-00420M: Universal Quadratic Forms and Class Numbers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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