Related papers: Membership problems for positive one-relator group…

We prove that one-relator groups with negative immersions are hyperbolic and virtually special; this resolves a recent conjecture of Louder and Wilton. As a consequence, one-relator groups with negative immersions are residually finite,…

We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]),…

We introduce two families of two-generator one-relator groups called primitive extension groups and show that a one-relator group is hyperbolic if its primitive extension subgroups are hyperbolic. This reduces the problem of characterising…

The main results of this paper is to give a complete characterization of the automaticity of one-relator semigroups with length less than or equal to three. Let $S=sgp\langle A|u=v\rangle$ be a semigroup generated by a set…

We consider the complexity of deciding membership of a given finite semigroup to a fixed pseudovariety. While it is known that there exist pseudovarieties with NP-complete or even undecidable membership problems, for many well-known…

We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of…

We give an alternative description of the grammic monoid in terms of weakly increasing subsequences. Specifically, we show that words $u,v$ in the generators $\{1,\ldots, n\}$ determine the same element of the grammic monoid of rank $n$ if…

The submonoid membership problem for a finitely generated group $G$ is the decision problem, where for a given finitely generated submonoid $M$ of $G$ and a group element $g$ it is asked whether $g \in M$. In this paper, we prove that for a…

We consider blind, deterministic, finite automata equipped with a register which stores an element of a given monoid, and which is modified by right multiplication by monoid elements. We show that, for monoids M drawn from a large class…

In this paper, a connection between rewriting systems and embedding of monoids in groups is found. We show that if a group with a positive presentation has a complete rewriting system $\Re$ that satisfies the condition that each rule in…

We study the class of monoids that arise as the submonoid of right units of finitely presented special inverse monoids (SIMs). Gray and Ru\v{s}kuc (2024) gave the first example of a finitely presented SIM whose submonoid of right units does…

We generalise a key result of one-relator group theory, namely Magnus's Freiheitssatz, to partially commutative groups, under sufficiently strong conditions on the relator. The main theorem shows that under our conditions, on an element $r$…

We investigate the Membership Problem for hypergeometric sequences: given a hypergeometric sequence $\langle u_n \rangle_{n=0}^\infty$ of rational numbers and a target $t \in \mathbb{Q}$, decide whether $t$ occurs in the sequence. We show…

In this paper we show that membership in finitely generated submonoids is undecidable for the free metabelian group of rank 2 and for the wreath product $\mathbb Z\wr (\mathbb Z\times \mathbb Z)$. We also show that subsemimodule membership…

We describe the automorphism groups of reductive monoids and of root monoids with active groups of invertible elements.

This is an English translation of three articles, originally written in German, by Wilhelm Magnus (1907--1990). The articles are from 1930, 1931, and 1932, respectively, and were the first articles published on one-relator group theory. The…

In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…

The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…

We give an infinite family of monoids $\Pi_N$ (for $N=2, 3, \dots$), each with a single defining relation of the form $bUa = a$, such that the Dehn function of $\Pi_N$ is at least exponential. More precisely, we prove that the Dehn function…

Multifraction reduction is a new approach to the word problem for Artin-Tits groups and, more generally, for the enveloping group of a monoid in which any two elements admit a greatest common divisor. This approach is based on a rewrite…