Existence of normal subgroups in finite p-groups

被引:5
|
作者
Glauberman, George [1 ]
机构
[1] Univ Chicago, Dept Math, Chicago, IL 60637 USA
关键词
finite p-group;
D O I
10.1016/j.jalgebra.2006.08.037
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Suppose p is a prime, S is a finite p-group, and B is a subgroup of S of order p(n) and class at most c. Does S possess a normal subgroup of order p(n) and class at most c? J. Alperin showed that the answer is negative in general. In this article, we show that the answer is affirmative if n is sufficiently small relative to P. (C) 2006 Elsevier Inc. All rights reserved.
引用
收藏
页码:800 / 805
页数:6
相关论文
共 50 条
  • [21] FINITE P-GROUPS WITH ISOMORPHIC SUBGROUPS
    CURRANO, JJ
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1973, 25 (01): : 1 - 13
  • [22] Quasinormal subgroups of finite p-groups
    Stonehewer, Stewart
    NOTE DI MATEMATICA, 2010, 30 : 93 - 99
  • [23] On the autocentralizer subgroups of finite p-groups
    Seifizadeh, Parisa
    Gholamian, Ali
    Farokhniaee, Amir Ali
    Nasrabadi, Mohammad Mehdi
    TURKISH JOURNAL OF MATHEMATICS, 2020, 44 (05) : 1802 - 1812
  • [24] ISOLATED SUBGROUPS OF FINITE p-GROUPS
    Song, Qiangwei
    An, Lijian
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2022, 105 (03) : 449 - 457
  • [25] The intersection of subgroups of finite p-groups
    Zhang, Qinhai
    Wei, Junjun
    ARCHIV DER MATHEMATIK, 2011, 96 (01) : 9 - 17
  • [26] ABELIAN SUBGROUPS OF FINITE P-GROUPS
    DANCS, SC
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 169 (NJUL) : 489 - &
  • [27] Normal subgroups of powerful p-groups
    Williams, James
    ISRAEL JOURNAL OF MATHEMATICS, 2020, 240 (01) : 267 - 273
  • [28] Normal subgroups of powerful p-groups
    James Williams
    Israel Journal of Mathematics, 2020, 240 : 267 - 273
  • [29] FINITE p-GROUPS WITH NON-NORMAL SUBGROUPS OF INDEX p IN THEIR NORMALIZERS
    Li, Xianhua
    Zhang, Junqiang
    COMMUNICATIONS IN ALGEBRA, 2011, 39 (06) : 2037 - 2043
  • [30] The finite p-groups with p conjugacy classes of non-normal subgroups
    Gustavo A. Fernández-Alcober
    Leire Legarreta
    Israel Journal of Mathematics, 2010, 180 : 189 - 192