On a strong form of Oliver's p-group conjecture
David J. Green, L\'aszl\'o H\'ethelyi, Nadia Mazza
TL;DR
This paper introduces a stronger version of Oliver's p-group conjecture, reformulates it using modular representation theory, and verifies it for Sylow p-subgroups of symmetric and general linear groups.
Contribution
It presents a new, stronger form of Oliver's p-group conjecture and connects it to modular representation theory, with verification for specific Sylow p-subgroups.
Findings
Strong form of Oliver's p-group conjecture introduced
Reformulation in terms of modular representation theory
Verification for Sylow p-subgroups of S_n and GL_n(F_q)
Abstract
We introduce a strong 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(F_q) satisfy both the strong conjecture and its reformulation.
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