University of Denver

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19962026

most citedThe Large Area Telescope on the Fermi Gamma-ray Space Telescope Mission

4.1k citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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46 papers · 1 filter

math.GR2022★ 2 cited

Abelianness and centrality in inverse semigroups

Michael Kinyon, David Stanovský

We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of…

math.GR2021★ 1 cited

From distributive l-monoids to l-groups, and back again

Almudena Colacito, Nikolaos Galatos, George Metcalfe +1

We prove that an inverse-free equation is valid in the variety LG of lattice-ordered groups (l-groups) if and only if it is valid in the variety DLM of distributive lattice-ordered…

math.GR2021★ 1 cited

A variety of Steiner loops satisfying Moufang's theorem: A solution to Rajah's Problem

Aleš Drápal, Petr Vojtěchovský

A loop $X$ is said to satisfy Moufang's theorem if for every $x, y, z \in X$ such that $x (y z) = (x y) z$ the subloop generated by $x$ , $y$ , $z$ is a group. We prove that the variety $V$ o…

math.GR2020★ 2 cited

Normality, nuclear squares and Osborn identities

Aleš Drápal, Michael Kinyon

Let $Q$ be a loop. If $S \leq Q$ is such that $φ (S) \subseteq S$ for each standard generator of $Inn (Q)$ , then $S$ does not have to be a normal subloop. In an LC loop the l…

math.GR2019

Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order

Izabella Stuhl, Petr Vojtěchovský

There is a one-to-one correspondence between involutory latin quandles and uniquely $2$ -divisible Bruck loops. Bruck loops of odd prime power order are centrally nilpotent. Using l…

math.GR2019

Bol loops and Bruck loops of order $pq$ up to isotopism

Petr Vojtěchovský

Let $p > q$ be odd primes. We classify Bol loops and Bruck loops of order $pq$ up to isotopism. When $q$ does not divide $p^{2} - 1$ , the only Bol loop (and hence the only Bruck loop) of…

math.GR2019★ 3 cited

Variants of epigroups and primary conjugacy

Maria Borralho, Michael Kinyon

In a semigroup $S$ with fixed $c \in S$ , one can construct a new semigroup $(S, \cdot_{c})$ called a \emph{variant} by defining $x \cdot_{c} y := x cy$ . Elements $a, b \in S$ are \emph{primari…

math.GR2019★ 15 cited

Involutive latin solutions of the Yang-Baxter equation

Marco Bonatto, Michael Kinyon, David Stanovský +1

Wolfgang Rump showed that there is a one-to-one correspondence between nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation and binary algebras in which all…

math.GR2018★ 11 cited

Conjugacy in inverse semigroups

Joao Araujo, Michael Kinyon, Janusz Konieczny

In a group $G$ , elements $a$ and $b$ are conjugate if there exists $g \in G$ such that $g^{- 1} a g = b$ . This conjugacy relation, which plays an important role in group theory, can be…

math.GR2017

Code loops in dimension at most 8

E. A. O'Brien, Petr Vojtěchovský

Code loops are certain Moufang $2$ -loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups. More preci…

math.GR2017

The multiplicative loops of Jha-Johnson semifields

S Pumpluen

The multiplicative loops of Jha-Johnson semifields are non-automorphic finite loops whose left and right nuclei are the multiplicative groups of a field extension of their centers.…

math.GR2017★ 3 cited

Commutativity theorems for groups and semigroups

Francisco Araújo, Michael Kinyon

In this note we prove a selection of commutativity theorems for various classes of semigroups. For instance, if in a separative or completely regular semigroup $S$ we have $x^p y^p…

math.GR2017★ 5 cited

Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids

João Araújo, Michael Kinyon, Janusz Konieczny +1

There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems fo…

math.GR2016★ 6 cited

Bol loops and Bruck loops of order $pq$

Michael Kinyon, Gábor P. Nagy, Petr Vojtěchovský

Right Bol loops are loops satisfying the identity $((z x) y) x = z ((x y) x)$ , and right Bruck loops are right Bol loops satisfying the identity $(x y)^{- 1} = x^{- 1} y^{- 1}$ . Let $p$ and $…

math.GR2015★ 4 cited

Central and medial quasigroups of small order

David Stanovský, Petr Vojtěchovský

We enumerate central and medial quasigroups of order less than $128$ up to isomorphism, with the exception of those quasigroups that are isotopic to $C_{4} \times C_{2}^{4}$ , $C_{2}^{6}$ , $C_…

math.GR2015

Abelian extensions and solvable loops

David Stanovský, Petr Vojtěchovský

Based on the recent development of commutator theory for loops, we provide both syntactic and semantic characterization of abelian normal subloops. We highlight the analogies betwe…

math.GR2015

Commutator theory for loops

David Stanovský, Petr Vojtěchovský

Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem o…

math.GR2015★ 1 cited

Commutative automorphic loops of order $p^{3}$

Dylene Agda Souza de Barros, Alexander Grishkov, Petr Vojtěchovský

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime $p$ , denote by $A_{p}$ the class of all $2$ -generated commutative automorphic loops $Q$ …

math.GR2015

Enumeration of nilpotent loops via cohomology

Daniel Daly, Petr Vojtěchovský

The isomorphism problem for centrally nilpotent loops can be tackled by methods of cohomology. We develop tools based on cohomology and linear algebra that either lend themselves t…

math.GR2015

Moufang loops with commuting inner mappings

Gábor P. Nagy, Petr Vojtěchovský

We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at m…

math.GR2015

Loops with abelian inner mapping groups: An application of automated deduction

Michael Kinyon, Robert Veroff, Petr Vojtěchovský

We describe a large-scale project in applied automated deduction concerned with the following problem of considerable interest in loop theory: If $Q$ is a loop with commuting inner…

math.GR2015★ 9 cited

Half-isomorphisms of Moufang loops

Michael Kinyon, Izabella Stuhl, Petr Vojtechovsky

We prove that if the squaring map in the factor loop of a Moufang loop $Q$ over its nucleus is surjective, then every half-isomorphism of $Q$ onto a Moufang loop is either an isomo…

math.GR2015★ 14 cited

Four Notions of Conjugacy for Abstract Semigroups

J. Araújo, Michael Kinyon, Janusz Konieczny +1

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been many attempts to find notions of c…

math.GR2013

Inverse semigroups with idempotent-fixing automorphisms

Joao Araujo, Michael Kinyon

A celebrated result of J. Thompson says that if a finite group $G$ has a fixed-point-free automorphism of prime order, then $G$ is nilpotent. The main purpose of this note is to ex…

Abelianness and centrality in inverse semigroups

From distributive l-monoids to l-groups, and back again

A variety of Steiner loops satisfying Moufang's theorem: A solution to Rajah's Problem

Normality, nuclear squares and Osborn identities

Enumeration of involutory latin quandles, Bruck loops and commutative automorphic loops of odd prime power order

Bol loops and Bruck loops of order pq up to isotopism

Variants of epigroups and primary conjugacy

Involutive latin solutions of the Yang-Baxter equation

Conjugacy in inverse semigroups

Code loops in dimension at most 8

The multiplicative loops of Jha-Johnson semifields

Commutativity theorems for groups and semigroups

Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids

Bol loops and Bruck loops of order pq

Central and medial quasigroups of small order

Abelian extensions and solvable loops

Commutator theory for loops

Commutative automorphic loops of order p3

Enumeration of nilpotent loops via cohomology

Moufang loops with commuting inner mappings

Loops with abelian inner mapping groups: An application of automated deduction

Half-isomorphisms of Moufang loops

Four Notions of Conjugacy for Abstract Semigroups

Inverse semigroups with idempotent-fixing automorphisms

Bol loops and Bruck loops of order $pq$ up to isotopism

Bol loops and Bruck loops of order $pq$

Commutative automorphic loops of order $p^{3}$