%0 Journal Article %T Symmetric cohomology of groups in low dimension %A Mihai D. Staic %J Mathematics %D 2009 %I arXiv %X We give an explicit characterization for group extensions that correspond to elements of the symmetric cohomology $HS^2(G,A)$. We also give conditions for the map $HS^n(G,A)\to H^n(G,A)$ to be injective. %U http://arxiv.org/abs/0912.0042v1