Groups with the weak minimal condition on non-normal non-abelian subgroups

被引：5
|
作者：
De Mari, Fausto [1 ]
机构：
[1] Univ Napoli Federico II, Naples, Italy
来源：
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY | 2020年 / 61卷 / 01期
关键词：
Metahamiltonian group; Minimax group; Weak minimal condition;
D O I：
10.1007/s13366-019-00450-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A group is called metahamiltonian if all its non-abelian subgroups are normal. It is proved here that a (generalized) soluble group satisfying the weak minimal condition on non-normal non-abelian subgroups is either minimax or metahamiltonian.
引用
收藏
页码：1 / 7
页数：7
相关论文
共 50 条
  • [31] Groups with the weak minimal condition for non-subnormal subgroups II
    Kurdachenko, Leonid A.
    Smith, Howard
    COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2005, 46 (04): : 601 - 605
  • [32] The Influence of the Number of Non-(sub)normal Non-abelian Subgroups on Solvability of Finite Groups
    Shi, Jiangtao
    Zhang, Cui
    ALGEBRA COLLOQUIUM, 2016, 23 (02) : 325 - 328
  • [33] M-normal subgroups and non-abelian lower continuous topological groups
    He, Wei
    Peng, Dekui
    MATHEMATISCHE NACHRICHTEN, 2021, 294 (08) : 1472 - 1483
  • [34] Weak approximation and non-abelian fundamental groups
    Harari, D
    ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2000, 33 (04): : 467 - 484
  • [35] On non-abelian C-minimal groups
    Simonetta, P
    ANNALS OF PURE AND APPLIED LOGIC, 2003, 122 (1-3) : 263 - 287
  • [36] On finite groups with few non-normal subgroups
    Mousavi, H
    COMMUNICATIONS IN ALGEBRA, 1999, 27 (07) : 3143 - 3151
  • [37] Groups with few non-normal cyclic subgroups
    Oggionni, Davide
    Ponzoni, Gianluca
    Zambelli, Vittoria
    NOTE DI MATEMATICA, 2010, 30 (02): : 121 - 133
  • [38] GROUPS WITH CONDITIONS OF INVARIANCE FOR INFINITE, NON-ABELIAN SUBGROUPS
    CHERNIKO.SM
    DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1970, (06): : 512 - &
  • [39] SNBAR-GROUPS WITH NON-ABELIAN FREE SUBGROUPS
    WILSON, JS
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1974, 7 (FEB): : 699 - 708
  • [40] Correction to: Groups with Invariant Infinite Non-Abelian Subgroups
    N. F. Kuzennyi
    S. S. Levchenko
    N. N. Semko
    Ukrainian Mathematical Journal, 2022, 73 : 1338 - 1338
12345