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

Jürgen Müller

paper

The projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_{4}$ revisited

arXiv:2511.00939

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 $1 1^{'}$ -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.

This is a direct sequel to the preprint arXiv:2509.05805 [math.RT] of mine. To make it sufficiently self-contained, a certain text overlap is unavoidable

The projective cover of the trivial module in characteristic 11 for the sporadic simple Janko group J4​ revisited

Abstract

The projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_{4}$ revisited