Acta mathematica scientia,Series B ›› 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

 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).

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

CLC Number: 

  • 20D15
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