Determining skew left braces of size np
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10507628" target="_blank" >RIV/00216208:11320/25:10507628 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Qr0Mu~9rvP" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Qr0Mu~9rvP</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00927872.2025.2499066" target="_blank" >10.1080/00927872.2025.2499066</a>
Alternative languages
Result language
angličtina
Original language name
Determining skew left braces of size np
Original language description
We define the twofold semidirect product of two skew left braces, in whichboth the additive and multiplicative groups are semidirect products of thecorresponding groups of the given skew left braces. We consider an odd primepand an integernsatisfyingpn,p|Aut(E)|for every groupEof ordernand such that each group of ordernphas a uniquep-Sylow subgroup. Underthese conditions, we prove that any skew left brace of sizenpis either a twofoldsemidirect product of the trivial brace of sizepand a skew left brace of sizenor a companion skew left brace of that one. We develop an algorithm to obtainall skew left braces of sizenpfrom the skew left braces of sizenand provide aformula to count them. We use this result to describe all skew left braces of size12pforp>=7, which proves a conjecture of V.G. Bardakov, M.V. Neshchadimand M.K. Yadav
Czech name
—
Czech description
—
Classification
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
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Communications in Algebra
ISSN
0092-7872
e-ISSN
1532-4125
Volume of the periodical
53
Issue of the periodical within the volume
11
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
4817-4843
UT code for WoS article
001485902900001
EID of the result in the Scopus database
2-s2.0-105004859458