Jordan’s theorem for solvable groups
Author:
Larry Dornhoff
Journal:
Proc. Amer. Math. Soc. 24 (1970), 533-537
MSC:
Primary 20.40
DOI:
https://doi.org/10.1090/S0002-9939-1970-0255680-1
MathSciNet review:
0255680
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
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