2016/07/04 by Ilaria Del Corso, Del Corso, I., Roberto Dvornicich +1 · 1 citation
Mathematics · #13A99 #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1607.00965
openalex publication_date 2016/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In \cite[Problem 72]Fuchs60 Fuchs asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases. The aim of the present paper is to address Fuchs' question when A is a \it finite characteristic ring. The result is a pretty good description of the groups which can occur as group of units in this case, equipped with examples showing that there are obstacles to a "short" complete classification. As a byproduct, we are able to classify all possible cardinalities of the group of units of a finite characteristic ring, so to answer Ditor's question \citeditor.