20.500.12556/RUL-148644 Rational Reidemeister trace of an outer automorphism of finite order Let $H$ 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. automorphism of finite order Reidemeister trace Hattori-Stallings rank Gottlieb’s theorem first order Euler characteristic Cooke’s obstruction avtomorfizem končnega reda Reidemeistrova sled Hattori-Stallingsov rang Gottliebov izrek Eulerjeva karakteristika prvega reda Cookova ovira true false true Angleški jezik Slovenski jezik Članek v reviji 2023-08-28 10:46:07 2023-08-28 10:46:09 2023-08-29 04:32:27 0000-00-00 00:00:00 2023 0 0 13 str. iss. 7, art. 107350 Vol. 227 Jul. 2023 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.54 0022-4049 10.1016/j.jpaa.2023.107350 141555715 1-s2.0-S0022404923000336-main.pdf 1-s2.0-S0022404923000336-main.pdf 1 9FC41030BF5AD4057B65DC1F1359F5EA 156417dfb105452ef64a54dd3e514dd3800b5dc5b026a20c32cb7309a7c28aa4 b4f509bc-4581-11ee-a605-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=172925 https://www.sciencedirect.com/science/article/pii/S0022404923000336 1 54ab9ab4-457f-11ee-a605-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=172924 Fakulteta za matematiko in fiziko 0 0 0