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On Groups All of whose 2-Blocks Have the Highest Defects

Published online by Cambridge University Press:  22 January 2016

Koichiro Harada
Koichiro Harada*
Affiliation:
Nagoya University
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If G is a finite group and p a fixed prime number, the irreducible representations of G are distributed into disjoint systems, the p-blocks. These blocks have been investigated especially by R. Brauer. In this note we are concerned with the problem: What is the structure of G which has only one p-block? Or more generally, what is the structure of G all of whose p-blocks have the highest defects?

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 283 - 286
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Brauer, R.: Some applications of the theory of blocks of characters of finite groups I, J. of Algebra, Vol. 1 (1964), pp. 152–167.CrossRefGoogle Scholar
[2] Burgoyne, N. and Fong, P.: The Schur multipliers of the Mathieu groups, Nagoya Math. J., Vol. 27 (1966), pp. 733–745.Google Scholar
[3] Curtis, C. and Reiner, I.: Representation theory of finite groups and associtaive algebras, New York, Interscience, 1962.Google Scholar
[4] Fong, P.: On the characters of p-solvable groups, Trans. Amer. Math. Soc. Vol. 98 (1961), pp. 263–284.Google Scholar
[5] Frobenius, G.: Über die Charaktere der mehrfach transitive Gruppen, Sitz. Preuss. Akad. Wissen. (1904), pp. 558–571.Google Scholar
[6] Hall, P. and Higman, G.: On the p-length of p-soluble groups and reduction theorems for Burnside’s problem, Proc. London Math. Soc. Vol. 6 (1956), pp. 1–42.Google Scholar
[7] Ito, N.: Über die Darstellungen der Permutationsgruppen von Primzahlgrad, Math. Zeitschr. Vol. 89 (1965), pp. 196–198.Google Scholar
[8] Suzuki, M.: Finite groups of even order in which Sylow 2-groups are independent, Ann. of Math., Vol. 80 (1964), pp. 58–77.Google Scholar