On Oliver’s p-group conjecture: II

Let p be an odd prime and S a finite p -group. B. Oliver’s conjecture arises from an open problem in the theory of p -local finite groups. It is the claim that a certain characteristic subgroup of S always contains the Thompson subgroup. In previous work the first two authors and M. Lilienthal recast Oliver’s conjecture as a statement about the representation theory of the factor group . We now verify the conjecture for a wide variety of groups .