Reidemeister spectrum of special and general linear groups over some fields contains 1

Abstract

We prove that if [Formula: see text] is an algebraically closed field of zero characteristic which has infinite transcendence degree over [Formula: see text], then there exists a field automorphism [Formula: see text] of [Formula: see text] and [Formula: see text] such that [Formula: see text]. This fact implies that [Formula: see text] and [Formula: see text] do not possess the [Formula: see text]-property. However, if the transcendece degree of [Formula: see text] over [Formula: see text] is finite, then [Formula: see text] and [Formula: see text] are known to possess the [Formula: see text]-property [13].