Abstract
Maximal 2-signalizers and centralizers of Sylow 2-subgroups in all finite simple groups are described. Also normalizers are computed for Sylow 2-subgroups in the finite simple groups of exceptional Lie type over a field of odd characteristic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
J. G. Thompson, “2-Signalizers of finite groups,” Pac. J. Math., 14, No. 1, 363–364 (1964).
V. D. Mazurov, “2-Signalizers in finite groups,” Algebra Logika, 7, No. 3, 60–62 (1968).
D. Gorenstein, Finite Simple Groups, An Introduction to Their Classification, Plenum, New York (1982).
Z. Janko and J. G. Thompson, “On a class of finite simple groups of Ree,” J. Alg., 4, No. 2, 274–292 (1966).
V. M. Levchuk and Ya. N. Nuzhin, “On the structure of Ree groups,” Algebra Logika, 24, No. 1, 26–41 (1985).
M. W. Liebeck and J. Saxl, “The primitive permutation groups of odd degree,” J. London Math. Soc., II. Ser., 31, No. 2, 250–264 (1985).
W. M. Kantor, “Primitive permutation groups of odd degree, and an application to finite projective planes,” J. Alg., 106, No. 1, 15–45 (1987).
M. Aschbacher, “On finite groups of Lie type and odd characteristic,” J. Alg., 66, No. 2, 400–424 (1980).
J. Conway, R. Curtis, S. Norton, et al., Atlas of Finite Groups, Clarendon, Oxford (1985).
M. Aschbacher, Finite Group Theory, Cambridge Univ. Press, Cambridge (1986).
R. W. Carter, Simple Groups of Lie Type, Pure Appl. Math., 28, Wiley, London (1972).
R. Steinberg, Lectures on Chevalley Groups, Yale University (1967).
Seminar on Algebraic Groups, Collected Papers, A. A. Kirillov (ed.), Mir, Moscow (1973).
M. Aschbacher, “A characterization of Chevalley groups over fields of odd order,” Ann. Math.(2), 106, Nos. 2/3, 353–468 (1977); “Correction,” Ann. Math. (2), 111, No. 3, 411–414 (1980).
M. E. Harris, “Finite groups containing an intrinsic 2-component of Chevalley type over a field of odd order,” Trans. Am. Math. Soc., 272, No. 1, 1–65 (1982).
M. W. Liebeck, J. Saxl, and G. M. Seitz, “Subgroups of maximal rank in finite exceptional groups of Lie type,” Proc. London Math. Soc., III. Ser., 65, No. 2, 297–325 (1985).
G. M. Seitz, “The root subgroups for maximal tori in finite groups of Lie type,” Pac. J. Math., 106, No. 1, 153–244 (1983).
G. M. Seitz, “Flag-transitive subgroups of Chevalley groups,” Ann. Math., 97, No. 1, 27–56 (1973).
A. Borel and J. Tits, “El´ements unipotents et sousgroupes paraboliques de groupes r´eductifs. I,” Inv. Math., 12, No. 2, 95–104 (1971).
D. Gorenstein and R. Lyons, The Local Structure of Finite Groups of Characteristic 2 Type, Mem. Am. Math. Soc., 42, No. 276, Am. Math. Soc., Providence, RI (1983).
M. Aschbacher, Overgroups of Sylow Subgroups in Sporadic Groups, Mem. Am. Math. Soc., 60, No. 343, Am. Math. Soc., Providence, RI (1986).
R. W. Carter and P. Fong, “The Sylow 2-subgroups of the finite classical groups,” J. Alg., 1, No. 1, 139–151 (1964).
L. E. Dickson, Linear Groups with an Exposition of the Galois Field Theory, Dover, New York (1958).
M. Aschbacher, “On the maximal subgroups of the finite classical groups,” Inv. Math., 76, No. 3, 469–514 (1984).
P. B. Kleidman, “The maximal subgroups of the finite 8-dimensional orthogonal groups PΏ +8 (q) and of their automorphism groups,” J. Alg., 66, No. 1, 173–242 (1987).
D. Gorenstein and K. Harada, “Finite simple groups of low rank and the families G2(q), D2 4(q), q Odd,” Bull. Am. Math. Soc., 77, No. 6, 829–862 (1971).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kondratiev, A.S., Mazurov, V.D. 2-Signalizers of Finite Simple Groups. Algebra and Logic 42, 333–348 (2003). https://doi.org/10.1023/A:1025923522954
Issue Date:
DOI: https://doi.org/10.1023/A:1025923522954