Every reasonably sized matrix group is a subgroup of S ∞

Robert Kallman

Fundamenta Mathematicae (2000)

  • Volume: 164, Issue: 1, page 35-40
  • ISSN: 0016-2736

Abstract

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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 ∞ .

How to cite

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Kallman, Robert. "Every reasonably sized matrix group is a subgroup of S ∞." Fundamenta Mathematicae 164.1 (2000): 35-40. <http://eudml.org/doc/212446>.

@article{Kallman2000,
abstract = {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 $S_∞$.},
author = {Kallman, Robert},
journal = {Fundamenta Mathematicae},
keywords = {infinite symmetric group; matrix groups; nonarchimedian absolute values; field extensions; topological groups; embeddings; general linear groups; projective special linear groups},
language = {eng},
number = {1},
pages = {35-40},
title = {Every reasonably sized matrix group is a subgroup of S ∞},
url = {http://eudml.org/doc/212446},
volume = {164},
year = {2000},
}

TY - JOUR
AU - Kallman, Robert
TI - Every reasonably sized matrix group is a subgroup of S ∞
JO - Fundamenta Mathematicae
PY - 2000
VL - 164
IS - 1
SP - 35
EP - 40
AB - 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 $S_∞$.
LA - eng
KW - infinite symmetric group; matrix groups; nonarchimedian absolute values; field extensions; topological groups; embeddings; general linear groups; projective special linear groups
UR - http://eudml.org/doc/212446
ER -

References

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  2. [2] N. Bourbaki, Commutative Algebra, Addison-Wesley, Reading, MA, 1972. 
  3. [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. Zbl0079.02802
  4. [4] J. Dieudonné, La géométrie des groupes classiques, 2nd ed., Springer, Berlin, 1963. 
  5. [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. Zbl0607.20003
  6. [6] N. Jacobson, Basic Algebra II, W. H. Freeman, San Francisco, 1980. 
  7. [7] I. Kaplansky, Fields and Rings, 2nd ed., Univ. of Chicago Press, Chicago, 1973. 
  8. [8] R. D. Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, 1981. Zbl0485.01013
  9. [9] J. Schreier und S. M. Ulam, Über die Permutationsgruppe der natürlichen Zahlenfolge, Studia Math. 4 (1933), 134-141. Zbl0008.20003
  10. [10] J.-P. Serre, Lie Algebras and Lie Groups, W. A. Benjamin, New York, 1965. 
  11. [11] S. M. Ulam, A Collection of Mathematical Problems, Wiley, New York, 1960. 
  12. [12] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1964. Zbl0137.24201

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