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^–1dt^–1 = 1 (a,b,c,d G, a² 1, c² 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.2000 Mathematics Subject Classification: 20E06