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每个Monolithic特征标至多零化两个共轭类的有限群

Finite Groups Whose Monolithic Characters Vanish on at Most Two Conjugacy Classes
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摘要 这篇文章研究了每个monolithic特征标至多零化两个共轭类的有限群,其结果推广了M.Bianchi,D.Chillag,和A.Gillio的一个定理。 The aim of this note is to classify the finite groups whose monolithic characters vanish on at most two conjugacy classes in the character table. Our result generalizes a theorem of M. Bianchi, D. Chillag and A. Gillio.
作者 张金山 施武杰 刘丹丹
机构地区 四川理工学院理学院 苏州大学数学科学学院
出处 《数学进展》 CSCD 北大核心 2009年第4期433-438,共6页 Advances in Mathematics（China）
基金 supported by the NSFC(No.10871032) the SRFDP of China(No.20060285002).
关键词 有限群 特征标 零元 finite groups character zeros
分类号 O152 [理学—基础数学]
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参考文献11

  • 1Berkovich, Y., On Isaacs' three character degrees theorem, Proc. Amer. Math. Sac., 1997, 125: 669-677.
  • 2Berkovich, Y. and Kazarin, L., Finite groups in which the zeros of every nonlinear irreducible character are conjugate modulo its kernel, Houston J. Math., 1998, 24: 619-630.
  • 3Bianchi, M., Chillag, D. and Gillio, A., Finite groups in which every irreducible character vanishes on at most two conjugacy classes, Houston J. Math., 2000, 26: 451-461.
  • 4Gorenstein, D., Finite Groups, Harper and Row, New York: 1968.
  • 5Isaacs, I.M., Characters of Finite Groups, Dover, New York: 1994.
  • 6Isaacs, I.M., Navarro, G. and Wolf, T.R., Finite group elements where no irreducible character vanishes, J. Algebra, 1999, 222: 413-423.
  • 7Moreto, A., On the number of conjugacy classes of zeros of characters, Israel J. Math., 2004, 142: 163-187.
  • 8Qian, G.H., Shi W.J. and You X.Z., Cojugacy classes outside a normal subgroup, Comm. Algebra, 2004, 12: 4809-4820.
  • 9Ren Y.C., Liu H., and Zhang J.S., On restriction and zeros of characters of finite groups, J. Sichuan Univ. Natural Science, in Chinese, 2007, 44: 1183-1188.
  • 10Sagirov, I.A., Finite groups having exactly two degrees of monolithic characters, Problems in the Theory of Groups and Homological Algebra (in Russian), Yaxoslavl' University, Yaroslavl, 1998, 213-220.
数学进展
2009年 第4期

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