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arXiv · 2608.16823

Groups with a Fixed Character Degree: The General Case

Mark Lewis·Brandon Martin
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Abstract

We obtain arithmetic conditions which are satisfied by solvable groups admitting an abelian $π$-subgroup. First, we extend a previous characterization by removing the square-free hypothesis on some fixed irreducible character degree. We then show the same arithmetic conditions follow from a faithful action of an abelian $π$-subgroup on the $π'$-part of the Fitting subgroup, where $π$ is the set of prime divisors of the aforementioned character degree.

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Mark Lewis, Brandon Martin. 2026-08-18. Groups with a Fixed Character Degree: The General Case. https://arxiv.org/abs/2608.16823

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