The Hopf invariant one theorem, sometimes also called Adams' theorem, is a deep theorem in homotopy theory which states that the only 
-spheres which are H-spaces are
,
,
,
and 
.
The theorem was proved by Adams (1958, 1960).
Hopf Invariant One Theorem
See also
H-Space, HomotopyExplore with Wolfram|Alpha
References
Adams, J. F. "On the Nonexistence of Elements of Hopf Invariant One." Bull. Amer. Math. Soc. 64, 279-282, 1958.Adams, J. F. "On the Nonexistence of Elements of Hopf Invariant One." Ann. Math. 72, 20-104, 1960.Referenced on Wolfram|Alpha
Hopf Invariant One TheoremCite this as:
Weisstein, Eric W. "Hopf Invariant One Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HopfInvariantOneTheorem.html