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Groups with a Cyclic Sylow Subgroup

Published online by Cambridge University Press:  22 January 2016

Walter Feit
Walter Feit*
Affiliation:
Yale University
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By focussing attention on indecomposable modular representations J. G. Thompson [11] has recently simplified and generalized some classical results of R. Brauer [1] concerning groups which have a Sylow group of prime order. In this paper this approach will be used to prove some results which generalize theorems of R. Brauer [2] and H. F. Tuan [12].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 571 - 584
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Brauer, R., Investigations on group characters, Ann. of Math. 42 (1941), 936–958.CrossRefGoogle Scholar
[2] Brauer, R., On groups whose order contains a prime number to the first power I, II, Am. J. Math. 64 (1942), 401–420, 421–440.CrossRefGoogle Scholar
[3] Curtis, and Reiner, , Representation Theory of Finite Groups and Associative Algebras, Interscience 1962.Google Scholar
[4] Feit, W., Groups which have a faithful representation of degree less than p-1, Trans. of A.M.S. 112 (1964), 287–303.Google Scholar
[5] Feit, W. and Thompson, J. G., Groups which have a faithful representation of degree less than . Pacific J. Math. 11 (1961), 1257–1262.CrossRefGoogle Scholar
[6] Green, J. A., The modular representation algebra of a finite group, 111. J. Math. 6 (1962), 607–619.Google Scholar
[7] Hall, P. and Higman, G., On the p-length of p-soluble groups and reduction theorems for Burnside’s problem, Proc. London Math. Soc., 6 (1956), 1–42.CrossRefGoogle Scholar
[8] Janko, Z., A new finite simple group with abelian 2-Sylow subgroups (to appear).Google Scholar
[9] Schur, I., Über die darstellung der symmetrischen und der alternierenden gruppen durch gebrochene lineare Substitutionen, J. Für Math. 139 (1911), 155–250.Google Scholar
[10] Swan, R. G., Periodic resolutions for finite groups, Ann. of Math. 72 (1960), 267–291.CrossRefGoogle Scholar
[11] Thompson, J. G., Vertices and Sources (to appear).Google Scholar
[12] Tuan, H. F., On groups whose orders contain a prime to the first power. Ann. of Math. 45 (1944), 110–140.CrossRefGoogle Scholar