Congruence classes of presentations for the complex reflection groups [formula omitted

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 , P S ) 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 P S is the set of all the basic relations on S.