Abstract
It is proved that the sectional two-rank of a finite group G having no subgroup of index two is at most four if a Sylow two-subgroup of the centralizer of some involution of G is of order 16. This implies the following assertion: If G is a finite simple group whose order is divisible by 25 and the order of the centralizer of some involution of G is not divisible by 25, then G is isomorphic to the Mathieu group M12 or the Hall-Janko group J2.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
V. V. Kabanov and V. M. Sitnikov, “Finite groups with a small Sylow two-subgroup in the centralizer of some involution,” in: 4th All-Union Symposium on Group Theory, Abstracts of Reports, Novosibirsk (1973), pp. 74–77.
D. Gorenstein and K. Harada, “Finite groups whose two-subgroups are generated by at most four elements,” Mem. Amer. Math. Soc.,147, 1–464 (1974).
S. A. Chunikhin, Subgroups of Finite Groups [in Russian], Nauka i Tekhnika, Minsk (1964).
A. N. Fomin, “Finite two-groups in which the centralizer of some involution has order eight,” Matem. Zap. Ural. Univ.,8, No. 3, 122–132 (1973).
C. T. C. Wall, “On groups consisting mostly of involutions,” Proceedings of the Cambridge Philosophy Society,67, 251–262 (1970).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 18, No. 6, pp. 869–876, December, 1975.
Rights and permissions
About this article
Cite this article
Kabanov, V.V., Starostin, A.I. Finite groups in which a Sylow two-subgroup of the centralizer of some involution is of order 16. Mathematical Notes of the Academy of Sciences of the USSR 18, 1105–1108 (1975). https://doi.org/10.1007/BF01099990
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01099990