On Oliver's p-group conjecture

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 fo...

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Bibliographic Details
Published in:arXiv.org 2008-08
Main Authors: Green, David J, Héthelyi, László, Lilienthal, Markus
Format: Article
Language:English
Subjects:
Subgroups
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.0804.2763