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.
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