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A rigidity theorem for skew braces with multiplicative group \(S\times T\) | ||
| International Journal of Group Theory | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 15 مرداد 1405 | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2026.149148.2024 | ||
| نویسنده | ||
| Marco Damele* | ||
| University of Cagliari | ||
| چکیده | ||
| We prove a rigidity result for finite skew braces whose multiplicative group is the direct product of two finite non-abelian simple groups. More precisely, we show that if (B) is a finite skew brace with ((B,\cdot)\cong S\times T), where (S) and (T) are finite non-abelian simple groups, then the additive group ((B,+)) cannot be supersolvable. This result contributes to the study of the restrictions imposed by the multiplicative group on the additive group of a skew brace, a central question related to the Byott–Vendramin conjecture. The proof combines structural properties of supersolvable groups, the existence of characteristic Hall subgroups, and classification results on finite simple groups admitting subgroups of 2-power index. These tools reduce the possible multiplicative groups to groups of projective linear type and force the occurrence of a section isomorphic to (\operatorname{PSL}_2(7)). The remaining cases are excluded through an analysis of suitable Sylow subgroups and the induced lambda action. | ||
| کلیدواژهها | ||
| Skew braces؛ supersolvable groups؛ non-abelian simple groups؛ Yang--Baxter equation | ||
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آمار تعداد مشاهده مقاله: 23 |
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