The Reflection Order In The Complex Reflection Group G(m,p,n)

Since Shephard and Todd classified all finite irreducible complex reflection groups in 1954[1],more and more people have made research on complex reflection groups.As the generalization of real reflection groups,there are many similar problems in complex reflection groups that have not been studied.For example,the reflection ordering on most complex reflection group.Jian-yi Shi has studied the reflection ordering on the imprimi-tive Complex groups G(m,1,n)and G(m,m,n).We will make an exploratory research on reflection ordering on the imprimitive complex reflection group G(m,p,n)(1<p<m)in this paper.We will give the necessary and sufficient conditions for the relation y<mp w between two elements y,in G(m,p,n)(1<p<m);We will study the properties of the set B(p)(w)=?y ? G(m,p,n)} y?mp w} for w in G(m,p,n);We will compute the set B(m)(w0)for the some special elements w0 in G(m,m,3)and G(m,m,4),and also all the chains in[e,w0].