Non-congruent Presentations For Certain Primitive Complex Reflection Groups

Professor Jian-yi Shi defined an equivalent relation among the simple root systems and a congruence relation among the presentations for finite complex reflection groups. He also gave all the inequivalent simple root systems and non-congruent presentations for G₁₂,G₂₄, G₂₅,G₂₆,G₁₉,G₁₁ and G₃₂. Then Li Wang gave the root system and all the inequivalent simple root systems for the primitive complex reflection groups G₁₃, G₂₂, G₂₉ and G₃₃ .In the present paper,I give representatives of all the congruent classes of presentations(or r.c.p for brevity)for them with the help of Li Wang's papers .And the main idea of methods adopts Professor Shi's.The proofs of my results are conceptional but with some help of the computer algebra software package GAP.