Exponential Genus Problems in One-relator Products of Groups

Erscheinungsjahr 2007
ISBN: 978-0-8218-3945-4
Verlag: American Mathematical Society

Buch, Englisch, 156 Seiten, Gewicht: 305 g

Reihe: Memoirs of the AMS number 873

Exponential equations in free groups were studied initially by Lyndon and Schutzenberger and then by Comerford and Edmunds. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper the author shows that for finite systems of quadratic exponential equations decidability passes, under certain hypotheses, from the factor groups to free products and one-relator products.

Autoren/Hrsg.

Duncan, A. J.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Introduction

Quadratic words

Quadratic exponential equations and ${mathcal L}$-genus

Resolutions of quadratic equations

Decision problems

Pictures

Corridors

Angle assignment

Curvature

Configurations $C$

Configurations $D$

Final angle adjustment

Isoperimetry

Proof of Theorem 5.9

Bibliography