On Grün's lemma for perfect skew braces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915953337434112 |
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| author | Tsang, Cindy |
| author_facet | Tsang, Cindy |
| contents | By previous work of Cedó, Smoktunowicz, and Vendramin, one already knows that the analog of Grün's lemma fails to hold for perfect skew left braces when the socle is used as an analog of the center of a group. In this paper, we use the annihilator instead of the socle. We shall show that the analog of Grün's lemma holds for perfect two-sided skew braces but not in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Grün's lemma for perfect skew braces Tsang, Cindy Group Theory Quantum Algebra Rings and Algebras By previous work of Cedó, Smoktunowicz, and Vendramin, one already knows that the analog of Grün's lemma fails to hold for perfect skew left braces when the socle is used as an analog of the center of a group. In this paper, we use the annihilator instead of the socle. We shall show that the analog of Grün's lemma holds for perfect two-sided skew braces but not in general. |
| title | On Grün's lemma for perfect skew braces |
| topic | Group Theory Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2409.18410 |