Euler characteristics and Möbius algebras of p-subgroup categories

Let G be a finite group and p a prime number. We compute the Euler characteristic in the sense of Leinster for some categories of nonidentity p-subgroups of G. The p-subgroup categories considered include the Brown poset , the transporter category , the linking category , the Frobenius, or fusion, category , and the orbit category of all nonidentity p-subgroups of G.