On skew braces and their ideals

We define combinatorial representations of finite skew braces and use this idea to produce a database of skew braces of small size. This database is then used to explore different concepts of the theory of skew braces such as ideals, series of ideals, prime and semiprime ideals, Baer and Wedderburn radicals and solvability. The paper contains several questions.

Citation

Konovalov , A , Smoktunowicz , A & Vendramin , L 2018 , ' On skew braces and their ideals ' , Experimental Mathematics , vol. Latest Articles . https://doi.org/10.1080/10586458.2018.1492476

Publication

Experimental Mathematics

Status

Peer reviewed

DOI

https://doi.org/10.1080/10586458.2018.1492476

ISSN

1058-6458

Type

Journal article

Rights

© 2018 Taylor & Francis Group, LLC. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at: https://doi.org/10.1080/10586458.2018.1492476

Description

The first-named author is partially supported by CCP CoDiMa (EP/M022641/1) and the OpenDreamKit Horizon 2020 European Research Infrastructures project (#676541). The second-named author is supported by the ERC Advanced grant 320974. The third-named author is supported by PICT-201-0147, MATH-AmSud 17MATH-01 and ERC Advanced grant 320974.