A characterization of odd order extensions of the finite projective symplectic groups 𝑃𝑆𝑝(4,𝑞)

Harris, Morton E.

doi:10.1090/S0002-9947-1972-0286897-4

A characterization of odd order extensions of the finite projective symplectic groups $\textrm {PSp}(4, q)$
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Trans. Amer. Math. Soc. 163 (1972), 311-327 Request permission

Abstract:

In a recent paper, W. J. Wong characterized the finite projective symplectic groups ${\text {PSp}}(4,q)$ where $q$ is a power of an odd prime integer by the structure of the centralizer of an involution in the center of a Sylow $2$-subgroup of ${\text {PSp}}(4,q)$. In the present paper, finite groups which contain an involution in the center of a Sylow $2$-subgroup whose centralizer has a more general structure than in the ${\text {PSp}}(4,q)$ case are classified by showing them to be odd ordered extensions of ${\text {PSp}}(4,q)$.

References

R. W. Carter, Simple groups and simple Lie algebras, J. London Math. Soc. 40 (1965), 193–240. MR 174655, DOI 10.1112/jlms/s1-40.1.193
Paul Fong and W. J. Wong, A characterization of the finite simple groups $\textrm {PSp} (4,q)$, $G_{2}(q)$, $D_{4}{}^{2}(q)$. I, Nagoya Math. J. 36 (1969), 143–184. MR 255666
Daniel Gorenstein and John H. Walter, On finite groups with dihedral Sylow 2-subgroups, Illinois J. Math. 6 (1962), 553–593. MR 142619
Daniel Gorenstein and John H. Walter, The characterization of finite groups with dihedral Sylow $2$-subgroups. I, J. Algebra 2 (1965), 85–151. MR 177032, DOI 10.1016/0021-8693(65)90027-X
B. Huppert, Endliche Gruppen. I, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
Donald Passman, Permutation groups, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0237627
Jacques Tits, Théorème de Bruhat et sous-groupes paraboliques, C. R. Acad. Sci. Paris 254 (1962), 2910–2912 (French). MR 138706
W. J. Wong, A characterization of the finite projective symplectic groups $\textrm {PSp}_{4}(q)$, Trans. Amer. Math. Soc. 139 (1969), 1–35. MR 252504, DOI 10.1090/S0002-9947-1969-0252504-X