Congruence classes of presentations for the complex reflection groups G(m, 1, n) and G(m,m,n

Abstract. We give an explicit description in terms of rooted graphs for representatives of all the congruence classes of presentations (or r.c.p. for brevity) for the imprimitive complex reflection group G(m, p, n). Also, we show that (S, PS) forms a presentation of G(m, p, n), where S is any generating reflection set of G(m, p, n) of minimally possible cardinality and PS is the set of all the basic relations on S. Introduction. In [7], we describe r.c.p. for two special families of imprimitive complex reflec-tion groups G(m, 1, n) and G(m,m, n) in terms of graphs. In the present paper, we shall extend the results to the imprimitive complex reflection group G(m, p, n) for any m, p, n ∈ N with p|m (read “ p divides m ”) and 1 < p < m