Jordan’s theorem for solvable groups

Dornhoff, Larry

doi:10.1090/S0002-9939-1970-0255680-1

Jordan’s theorem for solvable groups
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by Larry Dornhoff

Proc. Amer. Math. Soc. 24 (1970), 533-537

DOI: https://doi.org/10.1090/S0002-9939-1970-0255680-1

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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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