# Every reasonably sized matrix group is a subgroup of S ∞

Fundamenta Mathematicae (2000)

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

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topKallman, 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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- [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. Zbl0485.01013
- [9] J. Schreier und S. M. Ulam, Über die Permutationsgruppe der natürlichen Zahlenfolge, Studia Math. 4 (1933), 134-141. Zbl0008.20003
- [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. Zbl0137.24201

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