The Properties Of Three Elements Of Prime Alternating Knots And Braid Index Of The Composition Of Torus Links

This paper firstly studies the existence of prime number on alternating prime knot,such that x+y-2z= 0 (mod p) on every crossing,while x,y lable two understrand and z lables the overstrand.And I prove that knots remain this property under the Reidemeister moves.Then I promote braid index of the torus link.we know that all link have the form of braid,braid index is an important invariant of link,and it is an important means to study links.It is difficult to calculate the accurate braid index of the link,but we can calculate the upper and lower boundaries of the braid index.we can get the braid index of the composition of two links using the conclusion about the braid index of inequality and the conclusions of the braid index of torus link,and we can also get the the braid index of the composition of n links.