Abstract
A subgroup of H of a group G is called ss-quasinormally embedded in G if there exists a subgroup T of G such that G = HT and H ∩ T is squasinormally embedded in G. In this paper, we shall obtain some characterizations about p-nilpotency of G by assuming that some subgroups of prime power order of G are ss-quasinormally embedded in G.
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References
A. Ballester-Bolinches and M. C. Pedraza-Aguilera, Sufficient conditions for supersolvability of finite groups, J. Pure Appl. Algebra, 127 (1998), 113–118.
B. Huppert, Endiche Gruppen I, Springer-Verlag, Berlin, 1968.
D. J. S. Robinson, A course in the theory of groups, Spinger-Verlag, New York, 1982.
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.
F. Gross, Conjugacy of odd order Hall subgroups, Bull. London Math. Soc., 19 (1987), 311–319.
H. Wei and Y. Wang, On c*-normality and its properties, J. Group Theory, 10 (2007), 211–223.
K. Doerk and T. Hawkes, Finite Soluble Groups, Walter de Gruyter, Berlin-New York, 1992.
L. Miao, W. Guo and K. P. Shum, New criteria for p-nilpotency of finite groups, Comm. Algebra, 35 (2007), 965–974.
L. Miao, On complemented subgroups of finite groups, Czechoslovak Math. J., 56 (2006), 1019–1028.
M. Asaad and A. A. Heliel, On s-quasinormally embedded subgroups of finite groups, J. Pure Appl. Algebra, 165 (2001), 129–135.
M. Ramadan, M. E. Mohamed and A. A. Heliel, On c-normality of certain subgroups of prime power order of finite groups, Arch. Math., 85 (2005), 203–210.
O. H. Kegel, Sylow-Gruppen and subnormalteiler endlicher Gruppen, Math. Z., 78 (1962), 205–221.
P. Schmidt, Subgroups permutable with all Sylow subgroups, J. Algebra, 207 (1998), 285–293.
S. Li and Y. Li, On s-quasionormal and c-normal subgroups of a finie group, Czechoslovak Math. J., 58 (2008), 1083–1095.
W. Guo, The theory of classes of groups, Science Press-Kluwer Academic Publishers, Beijing-Boston, 2000.
X. Zhong and S. Li, On c-supplemented minimal subgroups of finite groups, Southeast Asian Bull. Math., 28 (2004), 1141–1148.
X. Guo and K. P. Shum, Finite p-nilpotent groups with some subgroups c-supplemented, J. Aust. Math. Soc., 78 (2005), 429–439.
X. Guo and K. P. Shum, On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups, Arch. Math., 80 (2003), 561–569.
X. Guo and K. P. Shum, On p-nilpotency of finite group with some subgroup csupplemented, Algebra Colloq., 10 (2003), 259–266.
X. Li and Z. Tao, Weakly normal subgroups of finite groups, Indian J. Pure Appl. Math., 41 (2010), 745–753.
Y. Wang, Finite groups with some subgroups of Sylow subgroups c-supplemented, J. Algebra, 224 (2000), 467–478.
Y. Li, Y. Wang and H. Wei, On p-nilpotency of finite groups with some subgroups π-quasinormally embedded, Acta. Math. Hungar, 108 (2005), 283–298.
Y. Wang, H. Wei and Y. Li, A generalization of Kramer’s theorem and its application, Bull. Aust. Math. Soc., 65 (2002), 467–475.
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The project is supported by the Natural Science Foundation of China (No:11071229) and the Natural Science Foundation of the Jiangsu Higher Education Institutions (No:10KJD110004).
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Li, C. Finite groups with some primary subgroups SS-quasinormally embedded. Indian J Pure Appl Math 42, 291–306 (2011). https://doi.org/10.1007/s13226-011-0020-x
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DOI: https://doi.org/10.1007/s13226-011-0020-x