English

A group-theoretic condition equivalent to a condition on principal blocks

Group Theory 2024-07-30 v2 Representation Theory

Abstract

In this note, we give a group-theoretic condition which is equivalent to the fact that the trivial character is the only complex irreducible character of a finite group G which is contained in the principal p-block for each prime p in a specified set of prime divisors of the order of G. This character-theoretic condition has been studied previously by a number of authors.

Keywords

Cite

@article{arxiv.2407.14517,
  title  = {A group-theoretic condition equivalent to a condition on principal blocks},
  author = {Geoffrey R. Robinson},
  journal= {arXiv preprint arXiv:2407.14517},
  year   = {2024}
}
R2 v1 2026-06-28T17:47:41.416Z