JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 25-32.doi: 10.6040/j.issn.1671-9352.0.2023.430

• Group Theory • Previous Articles    

Influence of σ-permutably embedded subgroups on p-nilpotency of finite groups

JI Jiuzhou, ZHOU Wei, YANG Nanying*   

  1. School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
  • Published:2025-05-19

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Abstract: Let G be a finite group. A subgroup A of G is said to be σ-permutable in G if G possesses a complete Hall σ-set H such that AH x=H xA for all H∈H and all x∈G. A subgroup H of G is said to be σ-permutably embedded in G if every Hall σi-subgroup of H is also a Hall σi-subgroup of some σ-permutable subgroup of G. By studying the σ-permutably embedded subgroups of Sylow p-subgroups of G, some new criteria for G to be a p-nilpotent group are given.

Key words: finite group, σ-permutable subgroup, σ-permutably embedded subgroup, p-nilpotent group

CLC Number: 

  • O152
[1] SKIBA A N. On σ-subnormal and σ-permutable subgroups of finite groups[J]. Journal of Algebra, 2015, 436:1-16.
[2] SKIBA A N. A generalization of a hall theorem[J]. Journal of Algebra and Its Applications, 2016, 15(5):207-214.
[3] KEGEL O H. Sylow-gruppen und subnormalteiler endlicher gruppen[J]. Mathematische Zeitschrift, 1962, 78:205-221.
[4] BALLESTER B A, PEDRAZA M C. Sufficient conditions for supersolubility of finite groups[J]. Journal of Pure and Applied Algebra, 1998, 127(2):113-118.
[5] ASAAD M, HELIEL A A. On s-quasinormally embedded subgroups of finite groups[J]. Journal of Pure and Applied Algebra, 2001, 165(2):129-135.
[6] LI Yangming, WANG Yanming. On π-quasinormally embedded subgroups of finite groups[J]. Journal of Algebra, 2004, 281(1):109-123.
[7] GUO W B, SKIBA A N. Finite groups with given s-embedded and n-embedded subgroups[J]. Journal of Algebra, 2009, 321(10):2843-2860.
[8] LI Yangming, QIAO Shouhong, WANG Yanming. On weakly s-permutably embedded subgroups of finite groups[J]. Communications in Algebra, 2009, 37(3):1086-1097.
[9] GUO W B, SKIBA A N. Groups with maximal subgroups of sylow subgroups σ-permutably embedded[J]. Journal of Group Theory, 2017, 20(1):169-183.
[10] LI Yangming, WANG Yanming, WEI Huaquan. On p-nilpotency of finite groups with some subgroups π-quasinormally embedded[J]. Acta Mathematica Hungarica, 2005, 108:283-298.
[11] HUPPERT B. Endliche gruppen Ⅰ[M]. Berlin: Springer, 1967.
[12] DOERK K, HAWKES T O. Finite soluble groups[M]. Berlin: Walter De Gruyter, 1992.
[13] GUO Wenbin. The theory of classes of groups[M]. Beijing: Science Press-Kluwer Academic Publishers, 2000.
[14] KNYAGINA V N, MONAKHOV V S. On the π'-properties of a finite group possessing a hall π-subgroup[J]. Siberian Mathematical Journal, 2011, 52(2):234-243.
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[4] CHEN Song-liang. On the structures of groups of order p2q3 with non-Abelian Sylow subgroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 93-97.
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