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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Jordan's theorem for solvable groups


Author: Larry Dornhoff
Journal: Proc. Amer. Math. Soc. 24 (1970), 533-537
MSC: Primary 20.40
MathSciNet review: 0255680
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Abstract: We show that every finite solvable group of $ n \times n$ matrices over the complex numbers has a normal abelian subgroup of index $ \leqq {2^{4n/3 - 1}}{3^{10n/9 - 1/3}}$. For infinitely many $ n$, this bound is best possible.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0255680-1
PII: S 0002-9939(1970)0255680-1
Keywords: Jordan's theorem, abelian normal subgroup, finite solvable group, solvable linear group, Fitting subgroup, primitive linear group
Article copyright: © Copyright 1970 American Mathematical Society