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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  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

NotesEmbed ?

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