数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (1): 131-138.doi: 10.1016/S0252-9602(12)60199-4

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FINITE p-GROUPS WHICH CONTAIN A SELF-CENTRALIZING CYCLIC NORMAL SUBGROUP

郝成功|靳竹萱   

  1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China； School of Mathematical Sciences, Peking University, Beijing 100871, China
  • 收稿日期:2011-10-09 出版日期:2013-01-20 发布日期:2013-01-20
  • 基金资助:

    Supported by the NSF of China (11171194) and by the NSF of Shanxi Province (2012011001-1).

FINITE p-GROUPS WHICH CONTAIN A SELF-CENTRALIZING CYCLIC NORMAL SUBGROUP

 HAO Cheng-Gong, JIN Zhu-Xuan   

  1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China； School of Mathematical Sciences, Peking University, Beijing 100871, China
  • Received:2011-10-09 Online:2013-01-20 Published:2013-01-20
  • Supported by:

    Supported by the NSF of China (11171194) and by the NSF of Shanxi Province (2012011001-1).

PDF (PC)

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摘要：

For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applica-tions are given, including a character theoretic description for such groups.

关键词: finite p-group, self-centralizing cyclic normal subgroup, 2-nilpotent group, cohomology group, irreducible complex character

Abstract:

For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applica-tions are given, including a character theoretic description for such groups.

Key words: finite p-group, self-centralizing cyclic normal subgroup, 2-nilpotent group, cohomology group, irreducible complex character

中图分类号: 

  • 20D15
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