This is related to this posting:


[complex cobordism from formal group laws?](https://mathoverflow.net/questions/5166/complex-cobordism-from-formal-group-laws)


but not entirely the same. I'd like to know if there are any proofs of Quillen's theorem that $\pi\_\* (MU)$ is the Lazard ring (home of the universal formal group law) other than Quillen's. Specifically, is it possible to prove the result without a deep understanding of the structure of $H^\*(MU)$ as a module over the Steenrod algebra?



Alternate proofs of Quillen's theorem on formal group laws and MU
Quillen's proof of this in the paper


*Elementary proofs of some results of cobordism theory using Steenrod operations*. Advances in Math. 7 1971 29–56 (1971)


does not make use of Adams spectral sequences or the structure of $H^\ast(MU)$ over the Steenrod algebra. In fact the only result from homotopy which is assumed is that the groups $MU^\ast(X)$ are finitely generated in each dimension.


