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

2017/08/21 by Timur Nasybullov, Nasybullov, Timur
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1708.06280

openalex publication_date 2017/08/21 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

We prove that if mathbbF is an algebraically closed field of zero\ncharacteristic which has infinite transcendence degree over \ℚ, then\nthere exists a field automorphism \φ of rm SL_n( mathbbF) and\n rm GL_n( mathbbF) such that R(\φ)=1. This fact implies that rm\nSL_n( mathbbF) and rm GL_n( mathbbF) do not possess the\nR_\∞-property. However, if the transcendece degree of mathbbF over\n\ℚ is finite, then rm SL_n( mathbbF) and rm\nGL_n( mathbbF) are known to possess the R_\∞-property.\n

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