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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

Infinite products of finite simple groups

Author(s): Jan Saxl; Saharon Shelah; Simon Thomas
Journal: Trans. Amer. Math. Soc. 348 (1996), 4611-4641.
MSC (1991): Primary 20E15, 20A15; Secondary 03E35, 20D06, 20E08
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Abstract: We classify the sequences $\langle S_{n} \mid n \in \mathbb {N} \rangle $ of finite simple nonabelian groups such that $\prod $$_{n}$ $ S_{n}$ has uncountable cofinality.


References:

[Ba]
H. Bass, Some remarks on group actions on trees, Comm. Algebra 4 (1976), 1091--1126. MR 54:7634

[Br]
J. L. Brenner, Covering theorems for FINASIGs. VIII: Almost all conjugacy classes in $\mathcal {A}_{n}$ have exponent $\leq 4$, J. Austral. Math. Soc. 25 (1978), 210--214. MR 58:872

[Ca1]
R. W. Carter, Simple Groups of Lie Type, Wiley, 1972. MR 53:10946

[Ca2]
R. W. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, Wiley, 1985. MR 87d:20060

[H]
W. Hodges, Model Theory, Encyclopedia of Mathematics and its Applications 42, Cambridge University Press, 1993. MR 94e:03002

[J]
T. Jech, Multiple Forcing, Cambridge University Press, 1986. MR 89h:03001

[Ko]
S. Koppelberg, Boolean algebras as unions of chains of subalgebras, Algebra Universalis 7 (1977), 195--203. MR 55:7878

[KT]
S. Koppelberg and J. Tits, Une propriété des produits directs infinis groupes finis isomorphes, C. R. Acad. Sci. Paris Sér. A 279 (1974), 583--585.

[Ku]
K. Kunen, Set Theory. An Introduction to Independence Proofs, North-Holland, Amsterdam, 1980. MR 82f:03001

[MN]
H. D. Macpherson and P. M. Neumann, Subgroups of infinite symmetric groups, J. London Math. Soc. (2) 42 (1990), 64--84. MR 92d:20006

[MSW]
G. Malle, J. Saxl and T. Weigel, Generation of classical groups, Geom. Dedicata 49 (1994), 85--116. MR 95d:20068

[Se]
J. P. Serre, Trees, Springer-Verlag, 1980. MR 82e:20083

[Sm]
C. Small, Arithmetic of Finite Fields, Marcel Dekker, 1991. MR 93i:11144

[ST1]
J. D. Sharp and S. Thomas, Uniformisation problems and the cofinality of the infinite symmetric group, Notre Dame Journal of Formal Logic 35 (1994), 328--345. CMP 1995:11

[ST2]
J. D. Sharp and S. Thomas, Unbounded families and the cofinality of the infinite symmetric group, Arch. Math. Logic 34 (1995), 33--45. CMP 1995:11

[Sh-b]
S. Shelah, Proper Forcing, Lecture Notes in Math 940, Springer-Verlag, Berlin, 1982. MR 84h:03002

[Sh-326]
S. Shelah, Vive la différence. I : Nonisomorphism of ultrapowers of countable models, in Set Theory of the Continuum, Mathematical Sciences Research Institute Publications 26, (ed. H. Judah, W. Just and H. Woodin), Springer-Verlag, 1992, pp. 357--405. MR 94g:03068

[Ta]
D. E. Taylor, The Geometry of the Classical Groups, Sigma Series in Pure Mathematics, Vol. 9, Heldermann Verlag, Berlin, 1992. MR 94d:20028

[Th]
S. Thomas, The cofinalities of the infinite dimensional classical groups, J. Algebra 179 (1996), 704--719. CMP 1996:7

[Ze]
D. Zelinsky, Every linear transformation is a sum of non-singular ones, Proc. Amer. Math. Soc 5 (1954), 627--630. MR 16:8c

[Zs]
K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math 3 (1892), 265--284.


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Additional Information:

Jan Saxl
Affiliation: Department of Pure Mathematics and Mathematical Statistics, Cambridge University, 16 Mill Lane, Cambridge CB2 1SB, England
Email: j.saxl@pmms.cam.ac.uk

Saharon Shelah
Affiliation: Department of Mathematics, The Hebrew University, Jerusalem, Israel
Address at time of publication: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: shelah@sunset.ma.huji.ac.il

Simon Thomas
Affiliation: Department of Mathematics, Bilkent University, Ankara, Turkey
Address at time of publication: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Email: sthomas@math.rutgers.edu

DOI: 10.1090/S0002-9947-96-01746-1
PII: S 0002-9947(96)01746-1
Received by editor(s): September 21, 1995
Additional Notes: The research of the second author was partially supported by the U.S.-Israel Binational Science Foundation. This paper is number 584 in the cumulative list of the second author's publications.
The research of the third author was partially supported by NSF Grants.
Copyright of article: Copyright 1996, American Mathematical Society


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