Abstract
This note is concerned with finite groups in which a Sylow two-subgroup S has an elementary Abelian subgroup E of order 22n, n≥2, such that E=A × z(S), ¦A¦=2n, and CS(a)=E for any involutiona ∈ A. It is proved that a simple group satisfying this condition is isomorphic to L3,(2n).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
K. Harada, “Finite simple groups with short chains of subgroups,” J. Math. Soc. Japan,20, No. 4, 655–672 (1968).
G. Glauberman, “Global and local properties of finite groups,” in: Finite Simple Groups, London-New York (1971).
V. D. Mazurov and S. A. Syskin, “A characterization of L3(2n) in terms of Sylow two-subgroups,” Izv. Akad. Nauk SSSR, Ser. Matem.,38, No. 3, 513–517 (1974).
J. Walter, “The characterization of finite groups with Abelian Sylow two-subgroups,” Ann. of Math.,89, 405–514 (1969).
D. Goldschmidt, “Two-fusion of finite groups,” Ann. of Math.,99, No. 1, 70–117 (1974).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 18, No. 6, pp. 861–868, December, 1975.
Rights and permissions
About this article
Cite this article
Il'inykh, A.P. A characterization of the groups L3(2n). Mathematical Notes of the Academy of Sciences of the USSR 18, 1101–1104 (1975). https://doi.org/10.1007/BF01099989
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01099989