English

Second cohomology groups and finite covers

Group Theory 2011-03-24 v2 Logic

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.

Keywords

Cite

@article{arxiv.0909.0366,
  title  = {Second cohomology groups and finite covers},
  author = {David M. Evans and Elisabetta Pastori},
  journal= {arXiv preprint arXiv:0909.0366},
  year   = {2011}
}

Comments

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

R2 v1 2026-06-21T13:41:34.503Z