Bounded Engel groups withall subgroups subnormal

被引：1
|
作者：
Smith, H [1 ]
机构：
[1] Bucknell Univ, Dept Math, Lewisburg, PA 17837 USA
来源：
COMMUNICATIONS IN ALGEBRA | 2002年 / 30卷 / 02期
关键词：
D O I：
10.1081/AGB-120013190
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is proved that if G is a group with all subgroups subnormal and G is a k-Engel group for some integer k then G is nilpotent.
引用
收藏
页码：907 / 909
页数：3
相关论文
共 50 条
  • [21] FINITE GROUPS WITH WEAKLY SUBNORMAL AND PARTIALLY SUBNORMAL SUBGROUPS
    Huang, J.
    Hu, B.
    Skiba, A. N.
    SIBERIAN MATHEMATICAL JOURNAL, 2021, 62 (01) : 169 - 177
  • [22] Finite Groups with Weakly Subnormal and Partially Subnormal Subgroups
    J. Huang
    B. Hu
    A. N. Skiba
    Siberian Mathematical Journal, 2021, 62 : 169 - 177
  • [23] Groups in which Sylow subgroups and subnormal subgroups permute
    Ballester-Bolinches, A
    Beidleman, JC
    Heineken, H
    ILLINOIS JOURNAL OF MATHEMATICS, 2003, 47 (1-2) : 63 - 69
  • [24] HYPERCENTRAL GROUPS WITH ALL SUBGROUPS SUBNORMAL
    SMITH, H
    BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1983, 15 (MAY) : 229 - 234
  • [25] Finite groups with modular σ-subnormal subgroups
    Liu, A-Ming
    Chen, Mingzhu
    Safonova, Inna N.
    Skiba, Alexander N.
    JOURNAL OF GROUP THEORY, 2024, 27 (03) : 595 - 610
  • [26] Permutable subnormal subgroups of finite groups
    Ballester-Bolinches, A.
    Beidleman, J. C.
    Cossey, John
    Esteban-Romero, R.
    Ragland, M. F.
    Schmidt, Jack
    ARCHIV DER MATHEMATIK, 2009, 92 (06) : 549 - 557
  • [27] On Finite Groups with Pπ-Subnormal Subgroups
    Vasil'eva, T. I.
    Koranchuk, A. G.
    MATHEMATICAL NOTES, 2023, 114 (3-4) : 421 - 432
  • [28] Finite groups with subnormal Schmidt subgroups
    Vedernikov, V. A.
    ALGEBRA AND LOGIC, 2007, 46 (06) : 363 - 372
  • [29] Non-subnormal subgroups of groups
    Zarrin, Mohammad
    JOURNAL OF PURE AND APPLIED ALGEBRA, 2013, 217 (05) : 851 - 853
  • [30] Finite groups with abnormal and -subnormal subgroups
    Monakhov, V. S.
    SIBERIAN MATHEMATICAL JOURNAL, 2016, 57 (02) : 352 - 363
12345