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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2024. Vol 49

Generation by Conjugate Elements of Finite Almost Simple Groups With a Sporadic Socle

Author(s)
Danila O. Revin1, Andrei V. Zavarnitsine2

1Siberian Federal University, Krasnoyarsk, Russian Federation

2Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russian Federation

Abstract
We study the minimum number of elements in the conjugacy class of an automorphism of a sporadic simple group that generate a subgroup containing all inner automorphisms. These results refine the estimates obtained earlier in the papers by Guralnick and Saxl and by Di Martino, Pellegrini, and Zalesski.
About the Authors

Danila O. Revin, Dr. Sci. (Phys.–Math.), Siberian Federal University, Krasnoyarsk, 660041, Russian Federation, revin@math.nsc.ru

Andrei V. Zavarnitsine, Dr. Sci. (Phys.–Math.), Sobolev Institute of Mathematics, Novosibirsk, Novosibirsk, 630090, Russian Federation, zav@math.nsc.ru

For citation

Revin D. O., Zavarnitsine A. V. Generation by Conjugate Elements of Finite Almost Simple Groups With a Sporadic Socle. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 49, pp. 135–142.

https://doi.org/10.26516/1997-7670.2024.49.135

Keywords
sporadic group, Fischer group, conjugacy, generators, Baer–Suzuki theorem
UDC
512.542
MSC
20E28, 20D20
DOI
https://doi.org/10.26516/1997-7670.2024.49.135
References
  1. Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A. Atlas of finite groups. Oxford, Clarendon Press, 1985.
  2. Di Martino L., Pellegrini M.A., Zalesski A.E. On generators and representations of the sporadic simple groups. Comm. Algebra, 2014, vol. 42, no. 2, pp. 880–908. https://doi.org/10.1080/00927872.2012.729629
  3. Flavell P., Guest S., Guralnick R. Characterizations of the solvable radical. Proc. Amer. Math. Soc., 2010, vol. 138, no. 4, pp. 1161–1170. https://doi.org/10.1090/S0002-9939-09-10066-7
  4. The GAP Group, GAP — Groups, Algorithms, and Programming, Version 4.12.2; 2022. http://www.gap-system.org
  5. Gordeev N., Grunewald F., Kunyavskii B., Plotkin E. A description of Baer–Suzuki type of the solvable radical of a finite group. J. Pure Appl. Algebra, 2009, vol. 213, no. 2, pp. 250–258. https://doi.org/10.1016/j.jpaa.2008.06.006
  6. Gordeev N., Grunewald F., Kunyavskii B., Plotkin E. Baer–Suzuki theorem for the solvable radical of a finite group. C. R. Acad. Sci. Paris, Ser. I, 2009, vol. 347, no. 5–6, pp. 217–222. https://doi.org/10.1016/j.crma.2009.01.004
  7. Gordeev N., Grunewald F., Kunyavskii B., Plotkin E. From Thompson to Baer– Suzuki: a sharp characterization of the solvable radical. J. Algebra, 2010, vol. 323, no. 10, pp. 2888–2904. https://doi.org/10.1016/j.jalgebra.2010.01.032
  8. Guest S. A solvable version of the Baer–Suzuki theorem. Trans. Amer. Math. Soc., 2010, vol. 362, pp. 5909–5946. https://doi.org/10.1090/S0002-9947-2010-04932-3
  9. Guest S., Levy D. Criteria for solvable radical membership via p-elements. J. Algebra, 2014, vol. 415, pp. 88–111. https://doi.org/10.1016/j.jalgebra.2014.06.003
  10. Guralnick R., Saxl J. Generation of finite almost simple groups by conjugates radical. J. Algebra, 2003, vol. 268, pp. 519–571. https://doi.org/10.1016/S0021-8693(03)00182-0
  11. Hall J., Soicher L. Presentations of some 3-transposition groups. Comm. Algebra, 1995, vol. 23, no. 7, pp. 2517–2559. https://doi.org/10.1080/00927879508825358
  12. Isaacs I. M. Character theory of finite groups. Providence, RI. AMS Chelsea. 2006. https://doi.org/10.1090/chel/359
  13. Isaacs I. M. Finite group theory. Grad. Stud. Math., 92. Providence, RI. AMS. 2008. https://doi.org/10.1090/gsm/092
  14. Norton S.P. Free transposition groups Comm. Algebra, 1996, vol. 24, no. 2, pp. 425–432. https://doi.org/10.1080/00927879608825578
  15. Revin D.O., Zavarnitsine A.V. On generations by conjugate elements in almost simple groups with socle 2F4(q 2 ) ′ . J. Group Theory, 2024, vol. 27, no. 1, pp. 119–140. https://doi.org/10.1515/jgth-2022-0216
  16. Wang Zh., Guo W., Revin D.O. Toward a sharp Baer–Suzuki theorem for the πradical: exeptional groups of small rank. Algebra and Logic, 2023, vol. 62, no. 1, pp. 1–21. https://doi.org/10.1007/s10469-023-09720-3
  17. Yang N., Revin D.O., Vdovin E.P. Baer–Suzuki theorem for the π-radical. Israel J. Math., 2021, vol. 245, no. 1, pp. 173–207. https://doi.org/10.1007/s11856-021-2209-y
  18. Yang N., Wu Zh., Revin D.O. On the sharp Baer–Suzuki theorem for the πradical: sporadic groups. Siberian Math. J., 2022, vol. 63, no. 2, pp. 387–394. https://doi.org/10.1134/S0037446622020161
  19. Yang N., Wu Zh., Revin D.O., Vdovin E.P. On the sharp Baer–Suzuki theorem for the π-radical of a finite group. Sb. Math., 2023, vol. 214, no. 1, pp. 108–147. https://doi.org/10.4213/sm9698e

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