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Normal p-subgroups of solvable linear groups

Published online by Cambridge University Press:  09 April 2009

John D. Dixon
John D. Dixon
Affiliation:
University of New South Wales
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In his paper [8], N. Itô gives an elegant proof that the Sylow p-group of a finite solvable linear group of degree n over the field of complex numbers is necessarily normal if p > n+1. Moreover he shows that this bound on p is the best possible when p is a Fermat prime (i.e. a prime of the form 2sk + 1) but that the bound may be improved to p > n when p is not a Fermat prime.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 4 , November 1967 , pp. 545 - 551
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Artin, E., Geometric Algebra, (Interscience 1957).Google Scholar
[2]Curtis, C. W. and Reiner, I., Representation Theory of Finite Groups and Associative Algebras, (Interscience 1962).Google Scholar
[3]Dixon, J. D., “The Fitting subgroup of a linear solvable group’, J. Australian Math. Soc. 7 (1967), 417–424.CrossRefGoogle Scholar
[4]Feit, W., “Groups which have a faithful representation of degree less than p—1”, Trans. Amer. Math. Soc. 112 (1964), 287–303.Google Scholar
[5]Fejt, W. and Thompson, J. G., “On groups which have a faithful representation of degree less than (ρ—1)/2”, Pacific J. Math. 11 (1961), 1257–1262.Google Scholar
[6]Huppert, B., “Lineare auflösbare Gruppen”, Math. Z. 67 (1957), 479–518.CrossRefGoogle Scholar
[7]Itô, N., “On the characters of soluble groups”, Nagoya Math. J. 3 (1951), 31–48.CrossRefGoogle Scholar
[8]Itô, N., “On a theorem of H. Blichfeldt”, Nagoya Math. J. 5 (1953), 75–78.CrossRefGoogle Scholar
[9]Suprunenko, D., “Soluble and Nilpotent Linear Groups”, Amer. Math. Soc. Transi. Math. Monographs vol. 9, 1963.Google Scholar