Bounds on the order of cross characteristic subgroups of the finite simple groups of Lie type

Asparouhov, Tihomir

doi:10.1090/S0002-9939-98-04745-5

Bounds on the order of cross characteristic subgroups of the finite simple groups of Lie type
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by Tihomir Asparouhov PDF

Proc. Amer. Math. Soc. 126 (1998), 3183-3189 Request permission

Abstract:

Let $X(r)$ and $G(q)$ be finite groups of Lie type and $r$ and $q$ be coprime. If $G(q)$ is embedded in $X(r)$, then the Landazuri-Seitz-Zalesskii theorem implies that $G(q)$ is small relative to $X(r)$. We formalize this observation and illustrate how it can be used with some applications.

References

Michael Aschbacher, On conjectures of Guralnick and Thompson, J. Algebra 135 (1990), no. 2, 277–343. MR 1080850, DOI 10.1016/0021-8693(90)90292-V
Bruce N. Cooperstein, Minimal degree for a permutation representation of a classical group, Israel J. Math. 30 (1978), no. 3, 213–235. MR 506701, DOI 10.1007/BF02761072
Robert M. Guralnick and John G. Thompson, Finite groups of genus zero, J. Algebra 131 (1990), no. 1, 303–341. MR 1055011, DOI 10.1016/0021-8693(90)90178-Q
Martin W. Liebeck, On the orders of maximal subgroups of the finite classical groups, Proc. London Math. Soc. (3) 50 (1985), no. 3, 426–446. MR 779398, DOI 10.1112/plms/s3-50.3.426
Martin W. Liebeck, Cheryl E. Praeger, and Jan Saxl, The maximal factorizations of the finite simple groups and their automorphism groups, Mem. Amer. Math. Soc. 86 (1990), no. 432, iv+151. MR 1016353, DOI 10.1090/memo/0432
M. Liebeck and J. Saxl, “On the orders of maximal subgroups of exceptional groups of Lie type", Proc LMS(2) 31 (1985), 237-249.
Kaoru Motose, On values of cyclotomic polynomials. II, Math. J. Okayama Univ. 37 (1995), 27–36 (1996). MR 1416242
Tanchu Shih, A note on groups of genus zero, Comm. Algebra 19 (1991), no. 10, 2813–2826. MR 1129542, DOI 10.1080/00927879108824294
Gary M. Seitz and Alexander E. Zalesskii, On the minimal degrees of projective representations of the finite Chevalley groups. II, J. Algebra 158 (1993), no. 1, 233–243. MR 1223676, DOI 10.1006/jabr.1993.1132
Pham Huu Tiep and Alexander E. Zalesskii, Minimal characters of the finite classical groups, Comm. Algebra 24 (1996), no. 6, 2093–2167. MR 1386030, DOI 10.1080/00927879608825690