A subgroup H of a group G is said to be weakly s-semipermutable in G if G has a subnormal subgroup T such that HT = G and H ∩ T ≤ \( {H}_{\overline{s}G} \), where \( {H}_{\overline{s}G} \) is the subgroup of H generated by all subgroups of H that are s-semipermutable in G. The main aim of the paper is to study the p-nilpotency of a group for which every second maximal subgroup of its Sylow p-subgroups is weakly s-semipermutable. Some new results are obtained.
Similar content being viewed by others
References
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, ATLAS of Finite Groups, Clarendon Press, Oxford (1985).
A. Delandtsheer, “Flage-transitive finite simple groups,” Arch. Math., 47, 395–400 (1986).
D. Gorenstein, Finite Simple Groups, Plenum Press, New-York–London (1982).
D. Gorenstein, The Classification of Finite Simple Groups. Vol. 1: Groups of Noncharacteristic 2 Type, Plenum Press, New-York–London (1983).
X. Y. Guo and K. P. Shum, “On c-normal subgroups of finite groups,” Publ. Math. Debrecen, 58, 85–92 (2001).
B. Huppert, Endliche Gruppen I, Springer, New York; Berlin (1967).
X. H. Li, Y. Xu, and T. Zhao, “Weakly s-semipermutable subgroups and p-nilpotency of finite groups (to appear).
Y. M. Li and X. H. Li, “ℨ-permutable subgroups and p-nilpotency of finite groups,” J. Pure Appl. Algebra, 202, 72–81 (2005).
A. N. Skiba, “A note on c-normal subgroups of finite groups,” Algebra Discrete Math., 3, 85–95 (2005).
L. F. Wang and Y. M. Wang, “On s-semipermutable maximal and minimal subgroups of Sylow p-subgroups of finite groups,” Comm. Algebra, 34, 143–149 (2006).
Y. M. Wang, “Finite groups with some subgroup of Sylow subgroups c-supplemented,” J. Algebra, 224, 467–478 (2000).
Y. Xu and X. H. Li, “On weakly s-semipermutable subgroups of finite groups,” Front. Math. China, 6, No. 1, 161–175 (2011).
Q. H. Zhang and L. F. Wang, “The influence of s-semipermutable properties of subgroups on the structure of finite groups,” Acta Math. Sinica, 48, No. 1, 81–88 (2005).
Y. D. Zhang, The Structure of Finite Groups, Chinese Sci. Press, Beijing (1982).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 5, pp. 694–698, May, 2014.
Rights and permissions
About this article
Cite this article
Xu, Y., Li, X.H. Second Maximal Subgroups of a Sylow p-Subgroup and the p-Nilpotency of Finite Groups. Ukr Math J 66, 775–780 (2014). https://doi.org/10.1007/s11253-014-0971-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-014-0971-2