DETERMINING ASCHBACHER CLASSES USING CHARACTERS
| Autor: | Sebastian Jambor |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Journal of the Australian Mathematical Society. 98:355-363 |
| ISSN: | 1446-8107 1446-7887 |
| DOI: | 10.1017/s144678871400055x |
| Popis: | Let ${\rm\Delta}:G\rightarrow \text{GL}(n,K)$ be an absolutely irreducible representation of an arbitrary group $G$ over an arbitrary field $K$; let ${\it\chi}:G\rightarrow K:g\mapsto \text{tr}({\rm\Delta}(g))$ be its character. In this paper, we assume knowledge of ${\it\chi}$ only, and study which properties of ${\rm\Delta}$ can be inferred. We prove criteria to decide whether ${\rm\Delta}$ preserves a form, is realizable over a subfield, or acts imprimitively on $K^{n\times 1}$. If $K$ is finite, we can decide whether the image of ${\rm\Delta}$ belongs to certain Aschbacher classes. |
| Databáze: | OpenAIRE |
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