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17.22 (2010)

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Suppose $A$ is a group which belongs to a variety $\mathfrak{V}$ of groups, and which is embeddable in the full symmetric group $S$ on an infinite set. Must the coproduct in $\mathfrak{V}$ of two copies of $A$ also be embeddable in $S$? (N. G. de Bruijn proved that this is true if $\mathfrak{V}$ is the variety of all groups.)

Contributor: G. M. Bergman

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