Every reasonably sized matrix group is a subgroup of $S_∞$

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

Every reasonably sized matrix group has an injective homomorphism into the group

S_{\infty}

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

S_{\infty}

.

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

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