Journal of Guangxi Normal University(Natural Science Edition) ›› 2018, Vol. 36 ›› Issue (1): 84-87.doi: 10.16088/j.issn.1001-6600.2018.01.011

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Notes on Frobenius Groups

LU Jiakuan*,LIU Xuexia,QIN Xueqing   

  1. College of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China
  • Received:2017-07-25 Online:2018-01-20 Published:2018-07-17

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Abstract: In this paper,a character theoretic condition characterizing finite Frobenius groups is obtained by using the relationship between the actions of finite groups on its irreducible characters and conjugacy classes. Furthermore,the following two results are obtained by using the structure of a special Frobenius group and the character theory of normal subgroups: ①If G is a finite solvable group,and every χ∈Irrm(G) is quasi-primitive,then G is abelian. ②If G is an M-group,and l=dl(G),the derived length of G,then G is a relative M-group with respect to G(l-1).

Key words: Frobenius groups, irreducible monomial character, solvable groups

CLC Number: 

  • O152.1
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