On Oliver's p-group conjecture

David J. Green
L\'aszl\'o H\'ethelyi
Markus Lilienthal

Submitted for publication, April 2008
Revised August 2008: Terminology now conforms to standard usage.

Abstract:
Let S be a p-group for an odd prime p.  Bob Oliver conjectures that a certain
characteristic subgroup X(S) always contains the Thompson subgroup J(S).
We obtain a reformulation of the conjecture as a statement about modular
representations of p-groups.  Using this we verify Oliver's conjecture for
groups where S/X(S) has nilpotence class at most two.