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arXiv · 1607.00965

Finite groups of units of finite characteristic rings

I. Del Corso·R. Dvornicich
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Abstract

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 \cite{ditor}.

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I. Del Corso, R. Dvornicich. 2016-07-04. Finite groups of units of finite characteristic rings. https://arxiv.org/abs/1607.00965

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