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

Geoffrey R. Robinson

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arXiv · 2407.14517

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

Geoffrey R. Robinson

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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.

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Geoffrey R. Robinson. 2024-07-03. A group-theoretic condition equivalent to a condition on principal blocks. https://arxiv.org/abs/2407.14517

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