The Cohomology of the Symmetric Groups

There are intimate connections between the homology and cohomology of the symmetric groups and algebraic topology. The first of these is their connection with the structure of cohomology operations. This arises through Steenrod’s definition of the Pth power operations in terms of properties of certain elements in the groups H_* (S _p ; $${\Bbb F}$$ _P ). Indeed, the original calculation of H _* (S _n ; $${\Bbb F}$$ _P ) by Nakaoka was motivated by this connection.