Is the projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_4$ a permutation module?

Jürgen Müller

doi:10.1016/j.jalgebra.2025.10.018

paper

Is the projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_{4}$ a permutation module?

arXiv:2509.05805 · doi:10.1016/j.jalgebra.2025.10.018

Abstract

We determine the ordinary character of the projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_{4}$ , and answer the question posed in the title.

Dedicated to the memory of Richard Parker. 18 pages. This version: Added a reference to the sequel arXiv:2511.00939 [math.RT], where the ambiguity left open at the end of this article is solved

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

Abstract

Is the projective cover of the trivial module in characteristic $11$ for the sporadic simple Janko group $J_{4}$ a permutation module?