Equivariant coincidence Nielsen numbers

The main thrust of this paper is to generalize certain aspects of equivariant Nielsen fixed point theory to coincidences, and to extend both equivariant fixed point, and coincidence point theory so as to include certain types of disconnected fixed point sets. These extensions allow us to exhibit certain important new examples, which enable us to utilize equivariant Nielsen theory in an essential way. In particular in these examples (unlike previous ones), the minimum number of coincidence points cannot be accurately estimated by other existing, or simpler, Nielsen theories. Also new is the inclusion of examples which illustrate the non-abelian side of the story. Finally, we fill a number of gaps and make corrections from earlier expositions in equivariant Nielsen theory.