Is the projective cover of the trivial module in characteristic 11 for the sporadic simple Janko group J₄ a permutation module?

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1. 1Reprint of: Is the projective cover of the trivial module in characteristic 11 for the sporadic simple Janko group J4 a permutation module?2026
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