3 citations · 8 across the 23 of their papers we have counts for
22 papers · 1 filter
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 …
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…
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…
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…
The Geometry of Special Monoids
Carl-Fredrik Nyberg-Brodda
A monoid is said to be special if it admits a presentation in which all defining relations are of the form . Groups are familiar examples of special monoids. This article st…