Rational Reidemeister trace of an outer automorphism of finite orderSmrekar, Jaka (Avtor) automorphism of finite orderReidemeister traceHattori-Stallings rankGottlieb’s theoremfirst order Euler characteristicCooke’s obstructionLet $H$ be a group of type $FP$ over the rationals and let $\phi\colon H\to H$ be an automorphism whose class in ${\rm Out}(H)$ has finite order and such that the Lefschetz number of some iterate $\phi^i$ is nonzero. We show that under a suitable Bass conjecture assumption, this iterate $\phi^i$ is conjugate to a finite order automorphism, and the intersection of the fixed point set of $\phi$ with the center of $H$ is of bounded exponent. In the torsion-free case it follows that the center of the HNN extension $\langle H,t\,\vert\,\forall h\in H:\,tht^{-1}=\phi(h)\rangle$ is infinite cyclic. These results are related to Geoghegan and Nicas' first order Euler characteristic of a group $G$ with a finite Eilenberg-MacLane complex; this is a morphism $\chi_1(G)$ from the center of $G$ to $H_1(G;k)$ where $k$ is a ring of coefficients. We give a complete determination of $\chi_1(G)$ with rational coefficients.20232023-08-28 10:46:07Članek v reviji148644sl