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arXiv · 2610.35603

Modular representations of metabelian groups

Lorenzo Traldi
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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.

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Lorenzo Traldi. 2026-10-26. Modular representations of metabelian groups. https://arxiv.org/abs/2610.35603

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