Representations of the double Burnside algebra and cohomology of the extraspecial p-group II.

Let E be the extraspecial p -group of order p 3 and exponent p where p is an odd prime. We determine the mod p cohomology H ⁎ ( X , F p ) of a summand X in the stable splitting of p -completed classifying space BE . In the previous paper (Hida and Yagita (2014) [7] ), we determined this cohomology modulo nilpotence. In this paper, we consider the whole of the cohomology. Moreover, we consider the stable splittings of BG for some finite groups with Sylow p -subgroup E related to the three dimensional linear group L 3 ( p ) . [ABSTRACT FROM AUTHOR]