Non-primitive Complex Reflection Groups G (m, L, N) Single Root And Expressed

Prof. Jian-yi Shi introduced an equivalent relation on simple root systems and a congruent relation among presentations for a complex reflection group. He also gave all the inequivalent simple root systems and all the non-congruent presentations for the complex reflection groups G12,G24,G25 and G26 in his paper [12]. In this paper, we find a relation between the isomorphism classes of rooted trees and all the inequivalent simple root systems of imprimitive complex reflection groups G(m, l,n). Then we give all the inequivalent simple root systems and all the non-congruent essential presentations of the imprimitive complex reflection groups G(m,1,n) (when n = 3, 4, 5).