The Reflection Order On The Complex Reflection Group G(m, P, N) (l

In[1],Shi Jian-Yi defined a partial ordering for imprimitive complex reflection group G(m,p,n),which is denoted by ≤mp,and called the reflection ordering on G(m,p,n).He studied the reflection ordering on the group G(m,1,n)in details.He described the form and the quantity of the elements in the set B(1)(w)=y{∈G(m,1,n)|y≤m1 w}.In[2],Shi Jian-Yi studied the reflection ordering on the group G(m,m,n).He gave a method to determine the elements in the set B(m)(w)={y∈G(m,m,n)|y≤mm w}.In this paper,we will study the reflection ordering on the group G(m,p,n)with 1<p<m.We will give a method to determine the elements in the set B(p)(w)={y∈G(m,p,n)|y≤mp w},following the way in[2].We will use this method to compute some special sets B(p)(w0)in the groups G(m,p,3)and G(m,p,4),where are some special elements in these groups.