Finite groups of non-prime-power order with exactly four character codegrees

2025/10/09 by Zeng, Yu, Ghaffarzadeh, Mehdi, Ghasemi, Mohsen +1
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2510.08221

Abstract

For an irreducible complex character \(χ\) of a finite group \(G\), the codegree of \(χ\) is defined as the ratio \(|G : ker(χ)| / χ(1)\), where \(ker(χ)\) represents the kernel of \(χ\). In this paper, we provide a detailed characterization of finite groups of non-prime power order that have exactly four irreducible character co-degrees.

Citations

• Character codegrees, kernels, and Fitting heights of solvable groups
• p-groups with exactly four codegrees
• Semi-extraspecial Groups

Related

• Finite groups in which every irreducible character has either p'-degree or p'-codegree
• p-groups with exactly four codegrees
• On the multiplicities of the character codegrees
• Finite groups with some bounded codegrees
• Finite groups with coprime non-linear codegrees