Geodesic
Generation by conjugate elements of finite almost simple groups with a sporadic socle
The Bulletin of Irkutsk State University. Series Mathematics, Tome 49 (2024), pp. 135-142 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: Fischer group, generators, Baer–Suzuki theorem.
Mots-clés : sporadic group, conjugacy 
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D. O. Revin; A. V. Zavarnitsine. Generation by conjugate elements of finite almost simple groups with a sporadic socle. The Bulletin of Irkutsk State University. Series Mathematics, Tome 49 (2024), pp. 135-142. http://geodesic.mathdoc.fr/item/IIGUM_2024_49_a9/

[1] Conway J.H., Curtis R.T., Norton S.P., Parker R.A., Wilson R.A., Atlas of finite groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[2] Di Martino L., Pellegrini M.A., Zalesski A.E., “On generators and representations of the sporadic simple groups”, Comm. Algebra, 42:2 (2014), 880–908 | DOI | MR | Zbl

[3] Flavell P., Guest S., Guralnick R., “Characterizations of the solvable radical”, Proc. Amer. Math. Soc., 138:4 (2010), 1161–1170 | DOI | MR | Zbl

[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, 213:2 (2009), 250–258 | DOI | MR | Zbl

[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, 347:5–6 (2009), 217–222 | DOI | MR | Zbl

[7] Gordeev N., Grunewald F., Kunyavskii B., Plotkin E., “From Thompson to Baer–Suzuki: a sharp characterization of the solvable radical”, J. Algebra, 323:10 (2010), 2888–2904 | DOI | MR | Zbl

[8] Guest S., “A solvable version of the Baer–Suzuki theorem”, Trans. Amer. Math. Soc., 362 (2010), 5909–5946 | DOI | MR | Zbl

[9] Guest S., Levy D., “Criteria for solvable radical membership via $p$-elements”, J. Algebra, 415 (2014), 88–111 | DOI | MR | Zbl

[10] Guralnick R., Saxl J., “Generation of finite almost simple groups by conjugates radical”, J. Algebra, 268 (2003), 519–571 | DOI | MR | Zbl

[11] Hall J., Soicher L., “Presentations of some $3$-transposition groups”, Comm. Algebra, 23:7 (1995), 2517–2559 | DOI | MR | Zbl

[12] Isaacs I. M., Character theory of finite groups, AMS Chelsea, Providence, RI, 2006 | DOI | MR | Zbl

[13] Isaacs I. M., Finite group theory, Grad. Stud. Math., 92, AMS, Providence, RI, 2008 | DOI | MR | Zbl

[14] Norton S.P., “Free transposition groups”, Comm. Algebra, 24:2 (1996), 425–432 | DOI | MR | Zbl

[15] Revin D.O., Zavarnitsine A.V., “On generations by conjugate elements in almost simple groups with socle ${}^2F_4(q^2)'$”, J. Group Theory, 27:1 (2024), 119–140 | DOI | MR | Zbl

[16] Wang Zh., Guo W., Revin D.O., “Toward a sharp Baer–Suzuki theorem for the $\pi$-radical: exeptional groups of small rank”, Algebra and Logic, 62:1 (2023), 1–21 | DOI | MR | Zbl

[17] Yang N., Revin D.O., Vdovin E.P., “Baer–Suzuki theorem for the $\pi$-radical”, Israel J. Math., 245:1 (2021), 173–207 | DOI | MR

[18] Yang N., Wu Zh., Revin D.O., “On the sharp Baer–Suzuki theorem for the $\pi$-radical: sporadic groups”, Siberian Math. J., 63:2 (2022), 387–394 | DOI | MR

[19] Yang N., Wu Zh., Revin D.O., Vdovin E.P., “On the sharp Baer–Suzuki theorem for the $\pi$-radical of a finite group”, Sb. Math., 214:1 (2023), 108–147 | DOI | MR | Zbl