3 citations · 8 across the 23 of their papers we have counts for
26 papers
Undecidability of the Diophantine problem for one-relator groups and one-relation monoids
Carl-Fredrik Nyberg-Brodda
We prove that the Diophantine problem, i.e. the problem of solving equations with coefficients, in one-relator groups and one-relation monoids is undecidable in general. Specifical…
Braid groups are not profinitely rigid
Carl-Fredrik Nyberg-Brodda
We show that the -strand braid group is not profinitely rigid when . We do this by exhibiting a family of pairwise non-isomorphic, finitely presented re…
On homological finiteness properties and free inverse monoids
Carl-Fredrik Nyberg-Brodda
We construct a simple and useful sufficient condition, based on actions on a lattice of idempotents, for monoids admitting homomorphisms to the monogenic free inverse monoid $\math…
The Baumslag-Gersten group and a problem of Olshanskii
Carl-Fredrik Nyberg-Brodda
We prove that a certain representation of the Baumslag-Gersten one-relator group by germs of continuous functions is not faithful. This gives a negative answer t…
On profinite rigidity, Grothendieck pairs, and the second homology of some -orbifold groups
Carl-Fredrik Nyberg-Brodda
The second homology group is of central importance in the study of profinite rigidity of -manifold groups. Although general and deep results imply that the integral homology of…
A note on right-angled Artin subgroups of one-relator groups
Carl-Fredrik Nyberg-Brodda
We give a short proof of the following result due to Howie: if is a right-angled Artin group embedding into some one-relator group, then is a finite forest. The proof on…
On the structure of groups defined by Kim and Manturov
Carl-Fredrik Nyberg-Brodda, Takuya Sakasai, Yuuki Tadokoro +1
We study the structure of a series of groups defined by Kim and Manturov. We show that the groups are finite for all and in fact they are 2-step nilpotent -gro…
On linguistic subsets of groups and monoids
André Carvalho, Carl-Fredrik Nyberg-Brodda
We study subsets of groups and monoids defined by language-theoretic means, generalizing the classical approach to the word problem. We expand on results by Herbst from 1991 to a m…
On the growth and integral (co)homology of free regular star-monoids
Carl-Fredrik Nyberg-Brodda
The free regular -monoid of rank is the freest -generated regular monoid in which every element has a distinguished pseudo-inverse …
G. S. Tseytin's seven-relation semigroup with undecidable word problem
Carl-Fredrik Nyberg-Brodda
We give an introduction to the ideas behind G. S. Tseytin's 1958 construction of a seven-relation semigroup with undecidable word problem. We give a history of the ideas leading up…
Membership problems for positive one-relator groups and one-relation monoids
Islam Foniqi, Robert D. Gray, Carl-Fredrik Nyberg-Brodda
Motivated by approaches to the word problem for one-relation monoids arising from work of Adian and Oganesian (1987), Guba (1997), and Ivanov, Margolis and Meakin (2001), we study…
Six Ukrainian articles on semigroup theory by A. K. Sushkevich
Carl-Fredrik Nyberg-Brodda
This is an English translation of six articles, originally written in Ukrainian, by the semigroup theorist Anton Kazimirovich Sushkevich (1889-1961). The articles date between 1935…
On the Dehn functions of a class of monadic one-relation monoids
Carl-Fredrik Nyberg-Brodda
We give an infinite family of monoids (for ), each with a single defining relation of the form , such that the Dehn function of is at least expo…
Tropical one-relation monoids
Carl-Fredrik Nyberg-Brodda
In 2010, Izhakian & Margolis proved that the bicyclic monoid admits a representation as a semigroup of upper triangular tropical matrices. We extend this result by classifying all…
On the Diophantine problem in some one-relator groups
Carl-Fredrik Nyberg-Brodda
We study the Diophantine problem, i.e. the decision problem of solving systems of equations, for some families of one-relator groups, and provide some background for why this probl…
The Adian-Rabin Theorem -- An English translation
Carl-Fredrik Nyberg-Brodda
This is an English translation of four remarkable articles, originally written in Russian, by Sergei Ivanovich Adian (1931--2020), supplemented by the translation of two closely re…
A word-hyperbolic special monoid with undecidable Diophantine problem
Carl-Fredrik Nyberg-Brodda
The Diophantine problem for a monoid is the decision problem to decide whether any given system of equations has a solution in . In this note, we give a simple example of a…
Multiplication tables and word-hyperbolicity in free products of semigroups, monoids, and groups
Carl-Fredrik Nyberg-Brodda
This article studies the properties of word-hyperbolic semigroups and monoids, i.e. those having context-free multiplication tables with respect to a regular combing, as defined by…
On the Word Problem for Free Products of Semigroups and Monoids
Carl-Fredrik Nyberg-Brodda
We study the language-theoretic aspects of the word problem, in the sense of Duncan & Gilman, of free products of semigroups and monoids. First, we provide algebraic tools for stud…
On one-relator groups and units of special one-relation inverse monoids
Carl-Fredrik Nyberg-Brodda
This note investigates and clarifies some connections between the theory of one-relator groups and special one-relation inverse monoids, i.e. those inverse monoids with a presentat…
Non-finitely Generated Maximal Subgroups of Context-free Monoids
Carl-Fredrik Nyberg-Brodda
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 maxima…
The Word Problem for One-relation Monoids: A Survey
Carl-Fredrik Nyberg-Brodda
This survey is intended to provide an overview of one of the oldest and most celebrated open problems in combinatorial algebra: the word problem for one-relation monoids. We provid…
On the Word Problem for Compressible Monoids
Carl-Fredrik Nyberg-Brodda
We study the language-theoretic properties of the word problem, in the sense of Duncan & Gilman, of weakly compressible monoids, as defined by Adian & Oganesian. We show that if $\…
On the Word Problem for Special Monoids
Carl-Fredrik Nyberg-Brodda
A monoid is called special if it admits a presentation in which all defining relations are of the form . Every group is special, but not every monoid is special. In this art…