Abstract
A subgroup H of a group G is said to be weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H ∩ T ≤ H sG , where H sG is the maximal s-permutable subgroup of G contained in H. In this paper, we investigate the influence of weakly s-supplemented subgroups on the structure of finite groups. Some recent results are generalized.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Asaad, Finite groups with certain subgroups of Sylow subgroups complemented, J. Algebra, 323 (2010), 1958–1965.
M. Asaad, On c-supplemented subgroups of finite groups, J. Algebra, 362(1–11) (2012).
A. Ballester-Bolinches and X. Guo, On complemented subgroups of finite groups, Arch. Math., 72 (1999), 161–166.
P. Hall, Complemented groups, J. London Math. Soc, 12 (1937), 201–204.
B. Huppert, Endliche Gruppen I, Berlin, Heidelberg, New York: Springer-Verlag, 1967.
O. H. Kegel, Sylow-Gruppen und Subnormalteiler endlicher Gruppen, Math. Z., 78(1962), 205–221.
D. Li and X. Guo, The influence of c-normality of subgroups on the structure of finite groups, J. Pure Appl. Algebra, 150 (2000), 53–60.
Y. Li and B. Li, On minimal weakly s-supplemented subgroups of finite groups, J. Algebra Appl., 10 (2011), 1–10.
L. Miao, On complemented subgroups of finite groups, Czechoslovak Mathematical Journal, 56 (2006), 1019–1028.
M. E. Mohamed, On weakly s-supplemented subgroups of finite groups The Arabian Journal for Science and Engineering, 35 (2010), 235–240.
S. Qiao, M. Isaacs and Y. Li, Complemented subgroups and p-nilpotence in finite groups, Arch. Math., 98 (2012), 403–411.
M. Short, Primitive soluble permutation groups of degree less than 256, Springer-Verlag Berlin Heidelberg, Berlin, 1992.
P. Schmid, Subgroups permutable with all Sylow subgroups, J. Algebra, 207 (1998), 285–293.
L. A. Shemetkov, Foundations of Finite Groups, Nauka, Main Editional Board for Physical and Mathematical Literature, Moscow, 1978.
A. N. Skiba, On weakly s-permutable subgroups of finite groups, J. Algebra, 315 (2007), 192–209.
K. Doerk and T. Hawkes, Finite Soluble Groups, Berlin, New York: Walter de Gruyter, (1992).
Y. Wang, Finite groups with some subgroups of Sylow subgroups c-supplemented, J. Algebra 224 (2000), 467–478.
M. Weinstein, Between Nilpotent and Solvable, Polygonal Publishing House, Passaic, NJ, (1982).
F. Xie, W. Guo and B. Li, On some open questions in theory of generalized permutable subgroups. Sci. China Ser. A, 39 (2009), 593–604.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Qiao, S. Weakly s-supplemented subgroups and p-nilpotency of finite groups. Indian J Pure Appl Math 44, 795–808 (2013). https://doi.org/10.1007/s13226-013-0043-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13226-013-0043-6