Every reasonably sized matrix group is a subgroup of S ∞
Kallman, Robert
Fundamenta Mathematicae, Tome 163 (2000), p. 35-40 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212446
@article{bwmeta1.element.bwnjournal-article-fmv164i1p35bwm,
     author = {Robert Kallman},
     title = {Every reasonably sized matrix group is a subgroup of S $\infty$},
     journal = {Fundamenta Mathematicae},
     volume = {163},
     year = {2000},
     pages = {35-40},
     zbl = {0967.20002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv164i1p35bwm}
}
Kallman, Robert. Every reasonably sized matrix group is a subgroup of S ∞. Fundamenta Mathematicae, Tome 163 (2000) pp. 35-40. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv164i1p35bwm/

[00000] [1] E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. | Zbl 0194.35301

[00001] [2] N. Bourbaki, Commutative Algebra, Addison-Wesley, Reading, MA, 1972.

[00002] [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. | Zbl 0079.02802

[00003] [4] J. Dieudonné, La géométrie des groupes classiques, 2nd ed., Springer, Berlin, 1963.

[00004] [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. | Zbl 0607.20003

[00005] [6] N. Jacobson, Basic Algebra II, W. H. Freeman, San Francisco, 1980.

[00006] [7] I. Kaplansky, Fields and Rings, 2nd ed., Univ. of Chicago Press, Chicago, 1973.

[00007] [8] R. D. Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, 1981. | Zbl 0485.01013

[00008] [9] J. Schreier und S. M. Ulam, Über die Permutationsgruppe der natürlichen Zahlenfolge, Studia Math. 4 (1933), 134-141. | Zbl 0008.20003

[00009] [10] J.-P. Serre, Lie Algebras and Lie Groups, W. A. Benjamin, New York, 1965.

[00010] [11] S. M. Ulam, A Collection of Mathematical Problems, Wiley, New York, 1960.

[00011] [12] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964. | Zbl 0137.24201