Non-finitely Generated Maximal Subgroups of Context-free Monoids
Group Theory
2021-11-02 v2 Rings and Algebras
Abstract
A finitely generated group or monoid is said to be context-free if it has context-free word problem. In this note, we give an example of a context-free monoid, none of whose maximal subgroups are finitely generated. This answers a question of Brough, Cain & Pfeiffer on whether the group of units of a context-free monoid is always finitely generated, and highlights some of the contrasts between context-free monoids and context-free groups.
Keywords
Cite
@article{arxiv.2107.12861,
title = {Non-finitely Generated Maximal Subgroups of Context-free Monoids},
author = {Carl-Fredrik Nyberg-Brodda},
journal= {arXiv preprint arXiv:2107.12861},
year = {2021}
}
Comments
10 pages, 51 references. Final submitted version