Research output: Research - peer-review › Article

- http://arxiv.org/abs/1408.4107
Accepted author manuscript

Igor Dolinka, Robert Duncan Gray, Jillian Dawn McPhee, James David Mitchell, Martyn Quick

We establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph *R*. As a consequence we show that, for any countable graph Γ, there are uncountably many maximal subgroups of the endomorphism monoid of *R* isomorphic to the automorphism group of Γ. Further structural information about End *R* is established including that Aut Γ arises in uncountably many ways as a Schützenberger group. Similar results are proved for the countable universal directed graph and the countable universal bipartite graph.

Original language | English |
---|---|

Pages (from-to) | 437-462 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 160 |

Issue number | 03 |

Early online date | 21 Jan 2016 |

DOIs | |

State | Published - May 2016 |

- Existentially closed graphs, Algebraically closed graphs, Random graph, Endomorphism monoid, Countable universal graph, Countable universal bipartite graph

**Discover related content**

Find related publications, people, projects and more using interactive charts.

## Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances

Mitchell, J. D., Morayne, M., Peresse, Y. H. & Quick, M. Sep 2010 In : Annals of Pure and Applied Logic. 161, 12, p. 1471-1485 15 p.Research output: Research - peer-review › Article

## Generating sequences of functions

Mitchell, J. D., Peresse, Y. & Quick, M. Mar 2007 In : Quarterly Journal of Mathematics. 58, 1, p. 71-79 9 p.Research output: Research - peer-review › Article

## Congruence lattices of finite diagram monoids

East, J., Mitchell, J. D., Ruskuc, N. & Torpey, M. 15 Jun 2018 In : Advances in Mathematics. 333, p. 931-1003 73 p.Research output: Research - peer-review › Article

## Maximal subsemigroups of finite transformation and diagram monoids

East, J., Kumar, J., Mitchell, J. D. & Wilson, W. A. 15 Jun 2018 In : Journal of Algebra. 504, p. 176-216Research output: Research - peer-review › Article

## Enumerating transformation semigroups

East, J., Egri-Nagy, A. & Mitchell, J. D. Aug 2017 In : Semigroup Forum. 95, 1, p. 109-125 17 p.Research output: Research - peer-review › Article

## The rank of the semigroup of transformations stabilising a partition of a finite set

Araujo, J., Bentz, W., Mitchell, J. D. & Schneider, C. 6 Jul 2015 In : Mathematical Proceedings of the Cambridge Philosophical Society.Research output: Research - peer-review › Article

## Micromeasure distributions and applications for conformally generated fractals

Fraser, J. M. & Pollicott, M. 2015 In : Mathematical Proceedings of the Cambridge Philosophical Society. 159, 3, p. 547-566 20 p.Research output: Research - peer-review › Article

## On the exact rate of convergence of frequencies of digits and local dimensions of multinomial measures

Olsen, L. O. R. 2015 In : Mathematical Proceedings of the Cambridge Philosophical Society. FirstView Article, 17 p.Research output: Research - peer-review › Article

## Hölder differentiability of self-conformal devil's staircases

Troscheit, S. 1 Mar 2014 In : Mathematical Proceedings of the Cambridge Philosophical Society. 156, 2, p. 295-311 17 p.Research output: Research - peer-review › Article

## Mathematical Proceedings of the Cambridge Philosophical Society (Journal)

Falconer, K. J. (Member of editorial board)1 Apr 2013 → …Activity: Publication peer-review and editorial work › Editor of research journal

ID: 21569010