  Let p be a prime number, G a finite group, and A a finite group acting on G.
The Brown poset of nonidentity p-subgroups of G is then an A-poset. We
investigate the equivariant subposet and the equivariant Euler characteristics
and establish a global relation between locally defined Euler characteristics
and the number of p-elements of G centralized by A. It is a consequence of this
relation that the equivariant version of Brown's theorem holds: The reduced
Euler characteristic of the A-equivariant Brown poset is divisible by the
p-part of the order of the centralizer of A. The second equivariant Euler
characteristic for the conjugation of G on the Brown poset for G is especially
intriguing because of its relation to the Knorr-Robinson conjecture and we
carry out a concrete numerical verification of the conjecture in case of the
smallest simple Mathieu group.
