|Dept.||National University of Ireland Galway|
Given a finite group G, the (G, G)-bisets form the double Burnside ring B(G, G) with multiplication given by "tensor product over G". Unlike the Burnside ring B(G), not much is known about the ring structure of B(G, G). Boltje and Danz (2013) gave a "ghost map" for B(G, G) over rationals when G is cyclic. I will describe their result in a more conceptual form and show how this approach can be applied to some noncyclic cases. This is a joint work with Goetz Pfeiffer and Brendan Masterson.