Abstract
A subgroup K of G is M p -supplemented in G if there exists a subgroup B of G such that G = KB and TB < G for every maximal subgroup T of K with |K: T| = p α. We study the structure of the chief factor of G by using M p -supplemented subgroups and generalize the results of Monakhov and Shnyparkov by involving the relevant results about the p-modular subgroup O p(G) of G.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Guo W., The Theory of Classes of Groups, Science Press–Kluwer Acad. Publ., Beijing, New York, Dordrecht, Boston, and London (2000).
Huppert B. and Blackburn N., Finite Groups. III, Springer-Verlag, Berlin and New York (1982).
Isaacs I. M., Finite Group Theory, Amer. Math. Soc., Providence (2008) (Grad. Stud. Math.; vol. 92).
Monakhov V. S. and Shnyparkov A. V., “On the p-supersolubility of a finite group with a µ-supplemented Sylow p-subgroup,” Sib. Math. J., vol. 50, no. 4, 681–686 (2009).
Tang J. and Miao L., “On M p-supplemented subgroups of finite groups,” Comm. Algebra, vol. 41, no. 5, 1913–1922 (2013).
Gao B., Tang J., and Miao L., “M p-Supplemented subgroups of finite groups,” Sib. Math. J., vol. 57, no. 1, 18–23 (2016).
Guo Y. and Isaacs I. M., “Conditions on p-subgroups iM plying p-nilpotence or p-supersolvability,” Arch. Math., vol. 105, no. 3, 215–222 (2015).
Ballester-Bolinches A., Esteban-Romero R., and Qiao S. H., “A note on a result of Guo and Isaacs about p-supersolubility of finite groups,” Arch. Math., vol. 106, no. 6, 501–506 (2016).
Xu M., An Introduction to Finite Groups, Science Press, Beijing (1999).
Guo W., Shum K. P., and Skiba A. N., “Criterions of supersolubility for products of supersoluble group,” Publ. Math. Debrecen, vol. 68, no. 3–4, 433–449 (2006).
Tate J., “Nilpotent quotient groups,” Topology, vol. 3, Suppl. 1, 109–111 (1964).
Author information
Authors and Affiliations
Corresponding author
Additional information
Yining; Yangzhou; Wuxi. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 4, pp. 779–784, July–August, 2017
Rights and permissions
About this article
Cite this article
Gao, B., Miao, L. & Tang, J. Influence of M p -supplemented subgroups on the structure of p-modular subgroups. Sib Math J 58, 606–610 (2017). https://doi.org/10.1134/S0037446617040061
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0037446617040061