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Properties of element orders in covers for Ln(q) and Un(q)

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Abstract

We show that if a finite simple group G, isomorphic to PSLn(q) or PSUn(q) where either n ≠ 4 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 PSLn(q), n ≠ 4 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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    A. V. Zavarnitsine

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  1. A. V. Zavarnitsine
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Correspondence to A. V. Zavarnitsine.

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Original Russian Text Copyright © 2008 Zavarnitsine A. V.

The author was supported by the FAPESP (Brazil) (Grant 06/60766-3), the Russian Foundation for Basic Research (Grant 05-01-00797), and the Siberian Division of the Russian Academy of Sciences (Grant No. 29 for the Junior Scientists and the Integration Project 2006.1.2).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 2, pp. 308–321, March–April, 2008.

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Zavarnitsine, A.V. Properties of element orders in covers for Ln(q) and Un(q). Sib Math J 49, 246–256 (2008). https://doi.org/10.1007/s11202-008-0025-9

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  • DOI: https://doi.org/10.1007/s11202-008-0025-9

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