×

zbMATH — the first resource for mathematics

A characterization of orthogonal groups over GF(2). (English) Zbl 0426.20013

MSC:
20D05 Finite simple groups and their classification
20D06 Simple groups: alternating groups and groups of Lie type
20G40 Linear algebraic groups over finite fields
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aschbacher, M, On finite groups in which the generalized Fitting group of the centralizer of some involution is extraspecial, Illinois J. math., 21, 347-364, (1977) · Zbl 0358.20024
[2] Aschbacher, M; Seitz, G, Involutions in Chevalley groups over fields of even order, Nagoya math. J., 63, 1-91, (1976) · Zbl 0359.20014
[3] Bender, H, On groups with abelian Sylow 2-subgroups, Math. Z., 117, 164-176, (1970) · Zbl 0225.20012
[4] Dempwolff, U; Wong, S.K; Dempwolff, U; Wong, S.K, On finite groups whose centralizer of an involution has normal and abelian subgroups, II, J. algebra, J. algebra, 52, 210-217, (1978) · Zbl 0474.20006
[5] Glauberman, G, Central elements in core-free groups, J. algebra, 4, 403-420, (1966) · Zbl 0145.02802
[6] Gorenstein, D, Finite groups, (1967), Harper & Row New York · Zbl 0168.27203
[7] Gorenstein, D; Harada, K, Finite groups whose 2-subgroups are generated by at most 4 elements, Mem. amer. math. soc., 147, 1-464, (1974) · Zbl 0353.20008
[8] Griess, R, Schur multipliers of the known finite simple groups, Bull. amer. math. soc., 78, 68-71, (1972) · Zbl 0263.20008
[9] Holt, D, Transitive permutation groups in which an involution central in a Sylow 2-group fixes a unique point, (), 165-192 · Zbl 0382.20005
[10] Patterson, N, (), (unpublished)
[11] Reifart, A, On finite groups with large extra-special subgroups, I, J. algebra, 53, 452-470, (1978) · Zbl 0382.20014
[12] Reifart, A, On finite groups with large extra-special subgroups, II, J. algebra, 54, 273-289, (1978) · Zbl 0413.20011
[13] Smith, F, On groups with an involution z such that the generalized Fitting subgroup E of C(z) is extra-special and \(C(z)E ⊇ ( Out(E))′\), Comm. algebra, 5, 207-277, (1977), (3) · Zbl 0387.20018
[14] Smith, F, On finite groups with large extra-special 2-subgroups, J. algebra, 44, 477-487, (1977) · Zbl 0425.20014
[15] \scF. Smith, On transitive permutation groups in which a 2-central involution fixes a unique point, Comm. Algebra, in press. · Zbl 0407.20001
[16] \scS. Smith, A characterization of finite Lie groups of types E and 2E, J. Algebra in press.
[17] Smith, S, Large extra-special 2-subgroups of widths 4 and 6, J. algebra, 58, 251-281, (1979) · Zbl 0411.20009
[18] Suzuki, M, Characterization of linear groups, Bull. amer. math. soc., 75, 1043-1091, (1969) · Zbl 0202.02503
[19] Suzuki, M, A characterization of the orthogonal group over finite fields of characteristic two, (), (Proceedings, Sapporo 1973)
[20] \scJ. G. Thompson, Notes on extra-special 2-subgroups, unpublished.
[21] Timmesfeld, F.G, A characterization of the Chevalley and Steinberg groups over F2, Geom. dedic., 1, 169-323, (1973) · Zbl 0262.20015
[22] Timmesfeld, F.G, Groups generated by root-involutions, I, J. algebra, 33, 75-134, (1975) · Zbl 0293.20026
[23] Timmesfeld, F.G, Finite simple groups in which the generalized Fitting group of the centralizer of some involution is extra-special, Ann. of math., 107, 297-369, (1978) · Zbl 0405.20016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.