Year: 2026
Type: preprint
Abstract: Let $G$ be a finite group. We prove that the order of the abelianization $G/G'$ divides the order of $H^{2m}(G,\mathbb{Z})$ for every $m\geq1$. As a consequence, for a field $K$, nonvanishing of $Ext^1_{KG}(K,K)$ implies nonvanishing of $Ext^n_{KG}(K,K)$ for every $n\geq1$. This answers a conjecture by Erdmann, Klász and Marczinzik. We use this to show that the Hochschild cohomology of $KG$ is nonzero in every nonnegative degree whenever the characteristic of $K$ divides $|G|$.
Source: arXiv (Cornell University)
Authors: Cruz, Tiago, Marczinzik, Rene
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214044721