Acta mathematica scientia, Series B >
FINITE p-GROUPS WHICH CONTAIN A SELF-CENTRALIZING CYCLIC NORMAL SUBGROUP
Received date: 2011-10-09
Online published: 2013-01-20
Supported by
Supported by the NSF of China (11171194) and by the NSF of Shanxi Province (2012011001-1).
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.
HAO Cheng-Gong , JIN Zhu-Xuan . FINITE p-GROUPS WHICH CONTAIN A SELF-CENTRALIZING CYCLIC NORMAL SUBGROUP[J]. Acta mathematica scientia, Series B, 2013 , 33(1) : 131 -138 . DOI: 10.1016/S0252-9602(12)60199-4
[1] Gorenstein D. Finite Group. New York: Harper & Row Publishers, 1980
[2] Aschbacher M. Finite Group Theory. Cambridge University Press, 2000
[3] Newman M F, Xu Mingyao. Metacyclic groups of prime-power order (Research announcement). Adv Math (Beijing), 1988, 17: 106–107
[4] Xu Mingyao, Zhang Qinhai. A classification of metacyclic 2-groups. Algebra Colloq, 2006, 13: 25–34
[5] Robinson D J S. A Course in the Theory of Groups. New York, Heidelberg, Berlin: Springer-Verlag, 1982
[6] Isaacs I M. Character Theory of Finite Groups. New York: Academic Press, 1976
[7] Huppert B. Endliche Gruppen I. Berlin, Heidelberg, New York: Springer, 1967
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