The Reidemeister Spectrum of Finite Abelian Groups

For a finite abelian group A, the Reidemeister number of an endomorphism & phi; is the same as the number of fixed points of & phi;, and the Reidemeister spectrum of A is completely determined by the Reidemeister spectra of its Sylow p-subgroups. To compute the Reidemeister spectrum of a finite abelian p-group P, we introduce a new number associated to an automorphism & psi; of P that captures the number of fixed points of & psi; and its (additive) multiples, we provide upper and lower bounds for that number, and we prove that every power of p between those bounds occurs as such a number.