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A product decomposition of infinite symmetric groups

Author(s): Ákos Seress
Journal: Proc. Amer. Math. Soc. 131 (2003), 1681-1685.
MSC (2000): Primary 20B30
Posted: October 1, 2002
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Abstract: We prove that for any infinite $\kappa$, the full symmetric group $\mathrm {Sym}(\kappa)$ is the product of at most $14$ abelian subgroups. This is a strengthening of a recent result of M. Abért.

References:

[Ab]
M. Abért. Symmetric groups as products of abelian subgroups. Bull. London Math. Soc. 34 (2002), 451-456.

[AK]
M. Abért and T. Keleti. Shuffle the plane. Proc. Amer. Math. Soc. 130 (2002), 549-553.

[APP]
M. Abért, P. P. Pálfy, and L. Pyber. Groups of finite abelian width. Preprint.

[AFG]
B. Amberg, S. Franciosi, and F. de Giovannio. Products of groups. The Clarendon Press, Oxford, 1992. MR 94h:20001

[It]
N. Ito. Über das Produkt von zwei abelschen Gruppen. Math. Z. (62) 1955, 400-401. MR 17:125b

[Ko]
P. Komjáth. Five degrees of separation. Proc. Amer. Math. Soc. 130 (2002), 2413-2417.

[Lu]
A. Lubotzky. Subgroup growth and congruence subgroups. Invent. Math. 119 (1995), 267-295. MR 95m:20054

[Or]
O. Ore. Some remarks on commutators. Proc. Amer. Math. Soc. 2 (1951), 307-314. MR 12:671e

[PR]
V. Platonov and A. Rapinchuk. Abstract properties of $S$-arithmetic subgroups and the congruence subgroup problem. Izv. Russian Acad. Sci. Ser. Math. 56 (1992), 483-508. MR 93i:20052

[Ta]
O. I. Tavgen. Bounded generation of Chevalley groups over rings of algebraic $S$-integers. Math. USSR Izv. 36 (1991), 101-128. MR 91e:20036

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Additional Information:

Ákos Seress
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
Email: akos@math.ohio-state.edu

DOI: 10.1090/S0002-9939-02-06720-5
PII: S 0002-9939(02)06720-5
Received by editor(s): November 7, 2001
Received by editor(s) in revised form: January 15, 2002
Posted: October 1, 2002
Additional Notes: This research was partially supported by the NSF
Communicated by: Stephen D. Smith
Copyright of article: Copyright 2002, American Mathematical Society

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