The spectral sequence of a split extension and the cohomology of an extraspecial group of order p³ and exponent p

Abstract. Let (E_r,d_r ) be the LHS spectral sequence associated to a split extension 1-->H -->G -->G/H -->1 of finite groups with coefficients in a field k. We prove a version of a theorem of Charlap and Vasquez which gives an explicit formula for d₂. We then apply this to the case where p is an odd prime, k has characteristic p , G is extraspecial of order p³ and exponent p, and H is elementary abelian of order p² . We calculate the terms of the spectral sequence in this case and prove E₃=E (and if p =3, E₂=E).

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