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On Some Results in the Theory of Finite Partially Soluble Groups 被引量：15

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摘要 This article provides an overview of some recent results and ideas relatedto the study of finite groups depending on the restrictions on some systems of theirsections.In particular,we discuss some properties of the lattice of all subgroups ofa finite group related with conditions of permutability and generalized subnormality for subgroups.The paper contains more than 30 open problems which were posed,atdifferent times,by some mathematicians working in the discussed direction.
作者 Alexander N.Skiba
机构地区 Department of Mathematics
出处 《Communications in Mathematics and Statistics》 SCIE 2016年第3期281-309,共29页 数学与统计通讯（英文）
关键词 Finite group.Subgroup lattice.G-covering subgroup system.I1-subnormal subgroup o-nilpotent group
分类号 O17 [理学—基础数学]
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  • 1Doerk, K., Hawkes, T.: Finite Soluble Groups, Walter de Gruyter, Berlin-New York, 1992.
  • 2Gaschiitz, W.: Prefrattinigruppen. Arch. Math., 13, 418-426 (1962).
  • 3Ezquerro, L. M.: A contribution to the theory of finite supersolvable groups. Rend. Sere. Mat. Univ. Padova, 89, 161-170 (1993).
  • 4Fan, Y., Guo, X., Shum, K. P.: Remarks on two generalizations of normality of subgroups. Chinese J. Contemp. Math., 27, 139-146 (2006).
  • 5Guo, X., Wang, J. X., Shum, K. P.: On Semi-Cover-Avoiding Maximal subgroups and Solvability of Finite Groups. Comm. Algebra, 34, 3235-3244 (2006).
  • 6Guo, X., Guo, P., Shum, K. P.: On semi cover-avoiding subgroups of finite groups. J. Pure and Applied Algebra, 209, 151-158 (2007).
  • 7Guo, X. Y., Wang, L. L.: On finite groups with some semi cover-avoiding subgroups. Acta Mathematica Sinica, English Series, 23, 1689-1696 (2007).
  • 8Wang, Y. M.: C-normality of groups and its properties. J. Algebra, 180, 954-965 (1996).
  • 9Johnson, D. L.: A note on supersoluble groups. Can. J. Math., 23, 562 564 (1971).
  • 10Ballester-Bolinches, A., Ezquerro, L. M.: Classes of Finite Groups, Springer, Dordrecht, 2006.

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Communications in Mathematics and Statistics
2016年 第3期

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