In [2], R.Bott and J.Milnor proved that the sphere Sⁿ is a parallelizable manifold if and only if n=1,3 or 7, J: F Adams proved above results and proved that Sⁿ is a Lie group for parallelizable manifold and also a H-space, naturally ones ask that Sⁿ  is a Lie Group for n= 0, 1,3 or 7? In this paper we prove that S⁷ is not a lie group, and it is not even a topological group. Therefore, Sⁿ  is a lie group (or a topologiacl group) if and only if n=0, 1,3.