The projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_4$ revisited

Jürgen Müller

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arXiv · 2511.00939

The projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_4$ revisited

Jürgen Müller

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Abstract

This is a sequel to arXiv:2509.05805 [math.RT], where we have determined the $11$-modular projective indecomposable summands of the permutation character of $J_4$ on the cosets of an $11'$-subgroup of maximal order, amongst them the projective cover of the trivial module, up to a certain parameter. Here, we fix this parameter, by applying a new condensation method for induced modules which uses enumeration techniques for long orbits.

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BibTeX RIS

Jürgen Müller. 2025-11-02. The projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_4$ revisited. https://arxiv.org/abs/2511.00939

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