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A Singular Equation of Length Four Over Groups

A Singular Equation of Length Four Over Groups Let G be a group and t an unknown. In this paper we prove that the equation atbtct −1 dt −1 = 1 (a,b,c,d ɛ G, a 2 ≠ 1, c 2 ≠ 1, bd ≠ 1) has a solution over G. This forms part of a program to investigate precisely when an equation, whose associated star graph contains no admissible paths of length less than 3, fails to have a solution over G. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Algebra Colloquium Springer Journals

A Singular Equation of Length Four Over Groups

Edjvet, M.
Algebra Colloquium , Volume 7 (3) – Jan 1, 2000
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28 pages

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Hong Kong
Subject
Mathematics; Algebra; Algebraic Geometry
ISSN
1005-3867
eISSN
0219-1733
DOI
10.1007/s10011-000-0247-2
Publisher site
See Article on Publisher Site

Abstract

Let G be a group and t an unknown. In this paper we prove that the equation atbtct −1 dt −1 = 1 (a,b,c,d ɛ G, a 2 ≠ 1, c 2 ≠ 1, bd ≠ 1) has a solution over G. This forms part of a program to investigate precisely when an equation, whose associated star graph contains no admissible paths of length less than 3, fails to have a solution over G.

Journal

Algebra Colloquium – Springer Journals

Published: Jan 1, 2000

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