arXiv subjects

Brandon Martin

Publications and source records attributed to Brandon Martin.

2 recordsLinked to original sources

arXiv2026

Groups with a Fixed Character Degree: The General Case

We obtain arithmetic conditions which are satisfied by solvable groups admitting an abelian $\pi$-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 $\pi$-subgroup on the $\pi'$-part of the Fitting subgroup, where $\pi$ is the set of prime divisors of the aforementioned character degree.

math.GR↗

arXiv2024

Groups with a Fixed Character Degree

This note is concerned with the question: for which positive integers $d,e$, with $d$ square-free and $\text{gcd}(d,d+e)=1$, does there exist a solvable (we will see, in our case, metabelian) group $G$, of order $|G|=d(d+e)$, such that $d$ is an irreducible character degree of $G$? The main theorem is an arithmetic characterization in terms of the prime divisors of $d(d+e)$. This work is motivated by previous investigations into finite groups $G$ that have an irreducible character of comparatively large degree.

math.GR↗