Second cohomology groups and finite covers

Mathematics – Group Theory

Scientific paper

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Typos corrected; change of title to 'Second cohomology groups and finite covers of infinite symmetric groups' in published ver

Scientific paper

10.1016/j.jalgebra.2010.12.004

For D an infinite set, k>1 and W the set of k-sets from D, there is a natural
closed permutation group G_k which is a non-split extension of \mathbb{Z}_2^W
by \Sym(D). We classify the closed subgroups of G_k which project onto
\Sym(D)$. The question arises in model theory as a problem about finite covers,
but here we formulate and solve it in algebraic terms.

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