Preprint
Aug 2026
On The Eaton-Moret\'o Conjecture for Principal Blocks of Finite Groups
Let $G$ be a finite group and let $p$ be a prime. If $P$ is a nonabelian Sylow $p$-subgroup of $G$ and $m(P)$ is the smallest non-linear irreducible character degree of $P$, we prove that there exists $\chi \in {\rm Irr}(G)$ in the principal $p$-block of $G$ such that $1<\chi(1)_p\le m(P)$, giving one inequality of the Eaton-Moret\'o conjecture for principal blocks. This, assuming Dade's Projective conjecture, implies the Eaton-Moret\'o conjecture for principal blocks.
Asier Arranz, J. Gómez-Serrano, Gabriel Navarro et al.
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