Every reasonably sized matrix group is a subgroup of S ∞

• Autorzy: Robert B. Kallman
• Języki publikacji: EN

Abstrakty

EN

Every reasonably sized matrix group has an injective homomorphism into the group $S_∞$ of all bijections of the natural numbers. However, not every reasonably sized simple group has an injective homomorphism into $S_∞$.

Słowa kluczowe

EN

infinite symmetric group; matrix groups; nonarchimedian absolute values; field extensions; topological groups

Kategorie tematyczne

• 20B30: Symmetric groups
• 12F99: None of the above, but in this section
• 12J25: Non-Archimedean valued fields
• 22A05: Structure of general topological groups
• 20H20: Other matrix groups over fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 164
• Numer: 1
• Strony: 35-40

Daty

wydano

2000

otrzymano

1999-01-08

poprawiono

2000-02-09

poprawiono

2000-03-11

Twórcy

autor

Robert B. Kallman

• Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430, U.S.A.

Bibliografia

• [1] E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967.
• [2] N. Bourbaki, Commutative Algebra, Addison-Wesley, Reading, MA, 1972.
• [3] N. G. de Bruijn, Embedding theorems for infinite groups, Indag. Math. 19 (1957), 560-569; Konink. Nederl. Akad. Wetensch. Proc. 60 (1957), 560-569.
• [4] J. Dieudonné, La géométrie des groupes classiques, 2nd ed., Springer, Berlin, 1963.
• [5] J. D. Dixon, P. M. Neumann and S. Thomas, Subgroups of small index in infinite symmetric groups, Bull. London Math. Soc. 18 (1986), 580-586.
• [6] N. Jacobson, Basic Algebra II, W. H. Freeman, San Francisco, 1980.
• [7] I. Kaplansky, Fields and Rings, 2nd ed., Univ. of Chicago Press, Chicago, 1973.
• [8] R. D. Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, 1981.
• [9] J. Schreier und S. M. Ulam, Über die Permutationsgruppe der natürlichen Zahlenfolge, Studia Math. 4 (1933), 134-141.
• [10] J.-P. Serre, Lie Algebras and Lie Groups, W. A. Benjamin, New York, 1965.
• [11] S. M. Ulam, A Collection of Mathematical Problems, Wiley, New York, 1960.
• [12] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964.