Finite skew braces with solvable additive group

Finite skew braces with solvable additive group Full article

Journal

Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X

Output data

Year: 2021, Volume: 574, Pages: 172-183 Pages count : 12 DOI: 10.1016/j.jalgebra.2021.01.027

Tags

Simple group; Skew brace; Solvable group

Authors

Gorshkov Ilya ¹ , Nasybullov Timur ^1,2

Affiliations

1	Sobolev Institute of Mathematics, Acad. Koptyug avenue 4, 630090 Novosibirsk, Russia
2	Novosibirsk State University

A.Smoktunowicz and L.Vendramin conjectured that if Ais a finite skew brace with solvable additive group, then the multiplicative group of A is solvable. In this short note we make a step towards positive solution of this conjecture proving that if A is a minimal finite skew brace with solvable additive group and non-solvable multiplicative group, then the multiplicative group of A is not simple. On the way to obtaining this result, we prove that the conjecture of A.Smoktunowicz and L.Vendramin is correct in the case when the order of A is not divisible by 3.

Gorshkov I. , Nasybullov T.
Finite skew braces with solvable additive group
Journal of Algebra. 2021. V.574. P.172-183. DOI: 10.1016/j.jalgebra.2021.01.027 WOS Scopus OpenAlex

Web of science:	WOS:000623913200008
Scopus:	2-s2.0-85100437429
OpenAlex:	W3127390092

DB	Citing
Scopus	6
OpenAlex	9
Web of science	6