Is the solvability of finite groups of order coprime to 15
essentially easier to prove than the entire Classification of Finite Simple Groups?



Solvability of finite groups of order coprime to 15 -- proof without using CFSG?
As Derek Holt has pointed out, the answer to the question is *yes*. --
Thompson proved that the only finite simple groups of order coprime to 3 are the
Suzuki groups, and Glauberman later extended this to a classification of
simple groups that do not have ${\rm S}\_3$ as a subgroup.
Both of these results are pre-classification, though they might not have been published.


