Vol. 2, No. 8, 2008
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On Oliver's p-group conjecture

David J. Green & László Héthelyi & Markus Lilienthal

Vol. 2 (2008), No. 8, 969-977
Abstract

Let S be a p-group for an odd prime p. B. 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.
Keywords

p-group, characteristic subgroup, Thompson subgroup, p-local finite group, Replacement Theorem

Mathematical Subject Classification

Primary: 20D15
Authors
David J. Green
Mathematical Institute
Friedrich-Schiller-Universität Jena
07737 Jena
Germany
László Héthelyi
Department of Algebra
Budapest University of Technology and Economics
Budapest, Pf. 91
H-1521
Hungary
Markus Lilienthal
FB Wirtschaftswissenschaften
Johann-Wolfgang-Goethe-Universität
House of Finance
Grüneburgplatz 1
60325 Frankfurt (Main)
Germany