Quadratic maps between non-abelian groups
| Autor: | Jamneshan, Asgar, Thom, Andreas |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | The aim of this article is to study quadratic maps, in the sense of Leibman, between non-abelian groups. As a key result, we provide a complete characterization of quadratic maps through a universal construction that can be computed explicitly. Applications include the classification of quadratic maps on finite abelian groups, proving the non-existence of polynomial maps of higher degree on perfect groups, establishing stability results for polynomial maps, and presenting a general inverse theorem for the Gowers norm with non-abelian coefficients on perfect groups with bounded commutator width. Comment: 21 pages |
| Databáze: | arXiv |
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