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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 2, Pages 308–321
(Mi smj1842)
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This article is cited in 18 scientific papers (total in 18 papers)
Properties of element orders in covers for $\operatorname L_n(q)$ and $\operatorname U_n(q)$
A. V. Zavarnitsine Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
We show that if a finite simple group $G$, isomorphic to $\operatorname{PSL}_n(q)$ or $\operatorname{PSU}_n(q)$ where either $n\ne4$ or $q$ is prime or even, acts on a vector space over a field of the defining characteristic of $G$; then the corresponding semidirect product contains an element whose order is distinct from every element order of $G$. We infer that the group $\operatorname{PSL}_n(q)$, $n\ne4$ or $q$ prime or even, is recognizable by spectrum from its covers thus giving a partial positive answer to Problem 14.60 from the Kourovka Notebook.
Keywords:
modular representation, weight, element order, recognition.
Received: 20.11.2007
Citation:
A. V. Zavarnitsine, “Properties of element orders in covers for $\operatorname L_n(q)$ and $\operatorname U_n(q)$”, Sibirsk. Mat. Zh., 49:2 (2008), 308–321; Siberian Math. J., 49:2 (2008), 246–256
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https://www.mathnet.ru/eng/smj1842 https://www.mathnet.ru/eng/smj/v49/i2/p308
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Abstract page: | 348 | Full-text PDF : | 105 | References: | 52 | First page: | 1 |
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