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Asier Arranz

Publications and source records attributed to Asier Arranz.

3 recordsLinked to original sources
arXiv2026

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.

math.RT↗
arXiv2026

Above Isaacs' Head Characters

The proof of the inductive McKay condition has been shown to imply that the character theory above the characters of degree not divisible by $p$ of a normal subgroup is locally determined. In this note, we establish a similar result for the Isaacs' head characters of a normal solvable subgroup of an arbitrary group. In particular, we give a new lower bound of the number of conjugacy classes of a finite group in terms of the Carter subgroups of any of its normal solvable subgroups.

math.GR↗