On a strong form of Oliver's p-group conjecture

David J. Green
Laszlo Hethelyi
Nadia Mazza

We introduce a stronger and more tractable form of Oliver's p-group
conjecture, and derive a reformulation in terms of the modular representation
theory of a quotient group. The Sylow p-subgroups of the symmetric group S_n
and of the general linear group GL(n,q)$ satisfy both the strong conjecture
and its reformulation.