On Oliver's p-group conjecture

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.

9 pages; terminology altered to conform to current usage

Cited by in corpus (4)

• On Oliver's p-group conjecture: II
• On a strong form of Oliver's p-group conjecture
• 2-subnormal quadratic offenders and Oliver's p-group conjecture
• Weak closure and Oliver's p-group conjecture