Group automorphisms of incidence algebras.

Let (P,≤) be an arbitrary partially ordered set and I(P) its incidence space. Then FI(P) denotes the associated finitary incidence algebra, where FI(P) = I(P) for locally finite posets (P,≤). We investigate the group of units U(FI(P)) of incidence algebras and its normal subgroups. This includes the structure and properties of maximal abelian, normal subgroups, and criteria for solvability and nilpotency. Lastly, we will classify the automorphism group of the group of units when (P,≤) = (Z,≤).