Finite alperin 2-groups with cyclic second commutants

被引：0
|
作者：
B. M. Veretennikov
机构：
[1] Ural State Technical University,
来源：
Algebra and Logic | 2011年 / 50卷
关键词：
2-group; Alperin group; commutant; representation of groups in terms of generators and defining relations;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
An Alperin group is a group in which every 2-generated subgroup has a cyclic commutant. Previously, we constructed examples of finite Alperin 2-groups with second commutant isomorphic to Z2 or Z4. Here, it is proved that for any natural n, there exists a finite Alperin 2-group whose second commutant is isomorphic to Z2n.
引用
收藏
页码：226 / 244
页数：18
相关论文
共 50 条
  • [21] Covering groups of nonconnected topological groups and 2-groups
    Rumynin, Dmitriy
    Vakhrameev, Demyan
    Westaway, Matthew
    COMMUNICATIONS IN ALGEBRA, 2019, 47 (12) : 5207 - 5217
  • [22] 2-groups and approximate fibrations
    Daverman, RJ
    Kim, Y
    TOPOLOGY AND ITS APPLICATIONS, 2002, 120 (1-2) : 9 - 21
  • [23] The neighbourhood of dihedral 2-groups
    Bálek, M
    Drápal, A
    Zhukavets, N
    ACTA APPLICANDAE MATHEMATICAE, 2005, 85 (1-3) : 25 - 33
  • [24] On Some Finite 2-Groups in which the Derived Group Has Two Generators
    Benjamin, Elliot
    Snyder, Chip
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2023, 73 (01) : 71 - 100
  • [25] On some finite 2-groups in which the derived group has two generators
    Elliot Benjamin
    Chip Snyder
    Czechoslovak Mathematical Journal, 2023, 73 : 71 - 100
  • [26] Conjugacy problem in a class of 2-groups
    Leonov, YG
    MATHEMATICAL NOTES, 1998, 64 (3-4) : 496 - 505
  • [27] A Class of Finite 2-groups G with Every Automorphism Fixing G /Φ (G) Elementwise
    Abdolzadeh, Hossein
    Sabzchi, Reza
    HOMOLOGICAL AND COMBINATORIAL METHODS IN ALGEBRA, 2018, 228 : 83 - 88
  • [28] On 2-groups of almost maximal class
    Baginski, C
    Konovalov, A
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2004, 65 (1-2): : 97 - 131
  • [29] The power structure of 2-generator 2-groups
    Kluempen, FL
    ALGEBRA COLLOQUIUM, 2002, 9 (03) : 287 - 302
  • [30] Constructions of difference sets in nonabelian 2-groups
    Applebaum, T.
    Clikeman, J.
    Davis, J. A.
    Dillon, J. F.
    Jedwab, J.
    Rabbani, T.
    Smith, K.
    Yolland, W.
    ALGEBRA & NUMBER THEORY, 2023, 17 (02) : 359 - 396
12345