Acta mathematica scientia, Series B >
A CHARACTERIZATION OF Mπ-GROUPS
Received date: 2012-05-04
Revised date: 2012-10-13
Online published: 2013-07-20
Supported by
Supported by NSF of China (11171169; 11071155) and the B.S. Foundation of Shandong Province (BS2012SF003).
Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs´s work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups.
Key words： Bπ′ -characters; Mπ-groups; π′-good pairs
HAI Jin-Ke , LI Zheng-Xing . A CHARACTERIZATION OF Mπ-GROUPS[J]. Acta mathematica scientia, Series B, 2013 , 33(4) : 1071 -1075 . DOI: 10.1016/S0252-9602(13)60064-8
[1] Isaacs I M. Primitive characters, normal subgroups and M-groups. Math Z, 1981, 177: 267–284
[2] Isaacs I M. Character Theory of Finite Groups. New York: Academic Press, 1976
[3] Parks A E. A group-theoretic characterization of M-groups. Proc Amer Math Soc, 1985, 94(2): 209–212
[4] Okuyama T. Module correspondence in finite groups. Hokkaido Math J, 1981, 10: 299–318
[5] Hanaki A. A characterization of Mp-groups. Proc Amer Math Soc, 1994, 121(2): 357–359
[6] Isaacs I M. Characters of -separable groups. J Algebra, 1984, 86: 98–128
[7] Nagao H, Tsushima Y. Representations of Finite Groups. New York: Academic Press, 1989
[8] Fan Y. On scott coefficients and block invariants: An approach for nonsplitting case. Comm Algebra, 1990, 18: 2199–2242
[9] Hanaki A, Hida A. A remarks on Mp-groups. Osaka J Math, 1992, 29: 71–74
[10] Hanaki A. On minimal non Mp-groups. Arch Math, 1993, 60: 316–320
[11] Huppert B. Character Theory of Finite Groups. Berlin, New York: Walter De Gruyter, 1998
[12] Hai J K, Li Z X. A note on M-groups. Acta Mathematica Sinica, Chinese Series, 2012, 55(4): 649–652
[13] Li Z X, Hai J K. Coleman automorphisms of semidirect products of Abelian groups by p-groups of maximal class. Acta Math Sci, 2012, 32A(2): 344–348
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