Second cohomology groups and finite covers

David M. Evans; Elisabetta Pastori

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Second cohomology groups and finite covers

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arxiv 0909.0366 v2 pith:AAJNNE3K submitted 2009-09-02 math.GR math.LO

David M. Evans , Elisabetta Pastori This is my paper

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keywords closedcoversfinitealgebraicarisesclassifycohomologyextension

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abstract

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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