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Recognition of the Finite Simple Groups F 4(2m) by Spectrum

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Abstract

The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F 4(2m) is recognizable by spectrum.

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References

  1. Mazurov V. D., “Recognition of finite groups by a set of orders of their elements,” Algebra i Logika, 37, No. 6, 371-379 (1998).

    Google Scholar 

  2. Shi W., “A characteristic property of PSL 2(7),” J. Austral. Math. Soc. Ser. A., 36, No. 3, 354-356 (1984).

    Google Scholar 

  3. Shi W., “A characteristic property of A 5,” J. Southwest-China Teach. Univ., 3, 11-14 (1986).

    Google Scholar 

  4. Shi W., “A characteristic property of J1 and PSL 2(2 n ),” Adv. Math., 16, 397-401 (1987).

    Google Scholar 

  5. Brandl R. and Shi W., “The characterization of PSL(2, q) by its element orders,” J. Algebra, 163, No. 1, 109-114 (1994).

    Google Scholar 

  6. Mazurov V. D., “Characterizations of groups by arithmetic properties,” Algebra Colloq., 11, No. 1, 129-140 (2004).

    Google Scholar 

  7. Mazurov V. D., “Recognition of finite simple groups S 4(q) by their element orders,” Algebra i Logika, 41, No. 2, 93-110 (2002).

    Google Scholar 

  8. Kondrat'ev A. S., “On prime graph components for finite simple groups,” Mat. Sb., 180, No. 6, 787-797 (1989).

    Google Scholar 

  9. Williams J. S., “Prime graph components of finite groups,” J. Algebra, 69, No. 2, 487-513 (1981).

    Google Scholar 

  10. Alekseeva O. A. and Kondrat'ev A. S., “Quasirecognition of one class of finite simple groups by the set of element orders,” Sibirsk. Mat. Zh., 44, No. 2, 195-207 (2003).

    Google Scholar 

  11. Mazurov V. D., “Characterization of finite groups by sets of all orders of the elements,” Algebra i Logika, 36, No. 1, 23-32 (1997).

    Google Scholar 

  12. Vasilyev A. V., “Minimal permutation representations of finite simple exceptional groups of types G 2 and F 4,” Algebra i Logika, 35, No. 6, 371-383 (1996).

    Google Scholar 

  13. Carter R. W., Simple Groups of Lie Type, John Wiley & Sons, London (1972).

    Google Scholar 

  14. Vasilyev A. V., “Recognizing groups G 2(3n) by their element orders,” Algebra i Logika, 41, No. 2, 74-80 (2002).

    Google Scholar 

  15. Steinberg R., Lectures on Chevalley Groups. Notes Prepared by John Faulkner and Robert Wilson, Yale University, New Haven, Conn. (1968).

    Google Scholar 

  16. Veldkamp F. D., “Representations of algebraic groups of type F 4 in characteristic 2,” J. Algebra, 16, No. 2, 326-339 (1970).

    Google Scholar 

  17. Shinoda K., “The conjugacy classes of Chevalley groups of type (F 4 ) over finite fields of characteristic 2,” J. Fac. Sci. Univ. Tokyo Sect. IA Math., 21, 133-159 (1974).

    Google Scholar 

  18. Zavarnitsin A. V., Element Orders in Coverings of the Groups L n(q) and Recognition of the Alternating Group A16 [in Russian] [Preprint, No. 48], NII Diskret. Mat. Inform., Novosibirsk (2000).

    Google Scholar 

  19. Jansen C., Lux K., Parker R. A., and Wilson R. A., An Atlas of Brauer Characters, Clarendon Press, Oxford (1995).

    Google Scholar 

  20. Conway J. H., Curtis R. T., Norton S. P., Parker R. A., and Wilson R. A., Atlas of Finite Groups, Clarendon Press, Oxford (1985).

    Google Scholar 

  21. Carter R. W., Finite Groups of Lie Type, John Wiley & Sons, New York (1985).

    Google Scholar 

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Cao, H.P., Chen, G., Grechkoseeva, M.A. et al. Recognition of the Finite Simple Groups F 4(2m) by Spectrum. Siberian Mathematical Journal 45, 1031–1035 (2004). https://doi.org/10.1023/B:SIMJ.0000048917.87625.c7

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  • DOI: https://doi.org/10.1023/B:SIMJ.0000048917.87625.c7

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