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SYMMETRIC GROUPS AS PRODUCTS OF ABELIAN SUBGROUPS

Published online by Cambridge University Press:  24 March 2003

MIKLÓS ABÉRT
MIKLÓS ABÉRT
Affiliation:
Department of Algebra and Number Theory, Eötvös University, Kecskeméti utca 10–12, H-1053 Budapest, [email protected]
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Abstract

A proof is given that the full symmetric group over any infinite set is the product of finitely many Abelian subgroups. In fact, 289 subgroups suffice. Sharp bounds are also obtained on the minimal number $k$ , such that the finite symmetric group $S_n$ is the product of $k$ Abelian subgroups. Using this, $S_n$ is proved to be the product of $72n^{1/2}(\log n)^{3/2}$ cyclic subgroups.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 4 , July 2002 , pp. 451 - 456
Copyright
© The London Mathematical Society 2002

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