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Strongly real elements in finite simple orthogonal groups

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Abstract

We prove the strong reality of an infinite series of groups and some elements of a special form in the simple real groups.

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References

  1. Tiep P. H. and Zalesski A. E., “Real conjugacy classes in algebraic groups and finite groups of Lie type,” J. Group Theory, 8, No. 3, 291–315 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  2. Bagiński C., “On sets of elements of the same order in the alternating group An,” Publ. Math. Debrecen, 34, 313–315 (1987).

    MATH  MathSciNet  Google Scholar 

  3. Kolesnikov S. G. and Nuzhin Ya. N., “On strong reality of finite simple groups,” Acta Appl. Math., 85, No. 1–3, 195–203 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  4. Gow R., “Commutators in the symplectic group,” Arch. Math. (Basel), 50, No. 3, 204–209 (1988).

    MATH  MathSciNet  Google Scholar 

  5. Gow R., “Products of two involutions in classical groups of characteristic 2,” J. Algebra, 71, No. 2, 583–591 (1981).

    Article  MATH  MathSciNet  Google Scholar 

  6. Ellers E. W. and Nolte W., “Bireflectionality of orthogonal and symplectic groups,” Arch. Math., 39, 113–118 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  7. Rämö J., “Strongly real elements of orthogonal groups in even characteristic,” J. Group Theory (to appear).

  8. Knüppel F. and Thomsen G., “Involutions and commutators in orthogonal groups,” J. Austral. Math. Soc., 65, No. 1, 1–36 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  9. Wonenburger M. J., “Transformations which are products of two involutions,” J. Math. Mech., 16, 327–338 (1966).

    MATH  MathSciNet  Google Scholar 

  10. Feit W. and Zuckerman G. J., “Reality properties of conjugacy classes in spin groups and symplectic groups,” Contemp. Math., 13, 239–253 (1982).

    MATH  MathSciNet  Google Scholar 

  11. Pham Huu Tiep and Zalesski A. E., “Unipotent elements of finite groups of Lie type and realization fields of their complex representations,” J. Algebra, 271, 327–390 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  12. Carter R. W., “Centralizers of semisimple elements in finite groups of Lie type,” Proc. London Math. Soc., 37, No. 3, 491–507 (1978).

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to A. A. Gal’t.

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Original Russian Text Copyright © 2010 Gal’t A. A.

The author was supported by the Russian Foundation for Basic Research (Grant 10-01-00391), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-344.2008.1), and the Russian Federal Agency for Education (Grant 2.1.1.419).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 2, pp. 241–248, March–April, 2010.

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Gal’t, A.A. Strongly real elements in finite simple orthogonal groups. Sib Math J 51, 193–198 (2010). https://doi.org/10.1007/s11202-010-0020-9

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  • DOI: https://doi.org/10.1007/s11202-010-0020-9

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