On Oliver's p-group conjecture: II

David J. Green
L\'aszl\'o H\'ethelyi
Nadia Mazza

Submitted for publication, January 2009

Abstract:
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 X(S) 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 S/X(S). We now verify the conjecture for a wide variety of groups
S/X(S).