Year: 2026
Type: preprint
Abstract: Let $M$ be a module over a commutative ring with unity $R$, and let $ϕ:M \to R$ be an $R$-linear map. Then the product $mn = m + (1+ϕ(m))n$ defines a monoid $Mon(ϕ)$ on $M$. We show that if $G$ is a group, then $G$ arises as the group of invertible elements of some such monoid $Mon(ϕ)$ if and only if $G$ is metabelian.
Source: arXiv (Cornell University)
Author: Traldi, Lorenzo
Institution: Lafayette College
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223908042