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.