Low-Degree Cohomology of Integral Specht Modules

We introduce a way of describing cohomology of the symmetric groups Σn with coefficients in Specht modules. We study H (Σn, S λ R) for i ∈ {0, 1, 2} and R = Z, Fp. The focus lies on the isomorphism type of H(Σn, S λ Z ). Unfortunately, only in few cases can we determine this exactly. In many cases we obtain only some information about the prime divisors of |H(Σn, S λ Z )|. The most important tools we use are the Zassenhaus algorithm, the Branching Rules, Bockstein type homomorphisms, and the results from [Burichenko et al., 1996].