PreprintCC BY-NC-ND 4.0arXiv
Modular representations of metabelian groups
Abstract
Let M be a module over a commutative ring with unity R, and let ϕ:M → 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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BibTeX
@misc{traldi2026modular,
title = {{Modular representations of metabelian groups}},
author = {Lorenzo Traldi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35603},
eprint = {2610.35603},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35603},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Modular representations of metabelian groups
AU - Lorenzo Traldi
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35603
UR - https://arxiv.org/abs/2610.35603
AB - Let M be a module over a commutative ring with unity R, and let ϕ:M → 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.
ER -