# PhD Studentship (Maths): The Relational Complexity of Finite Permutation Groups

**University of South Wales**

Qualification type: | PhD |

Location: | Pontypridd |

Funding for: | UK Students, EU Students |

Funding amount: | £14,553 plus tuition fees paid at the Home / EU rate (currently £4,195 per annum). |

Hours: | Full Time |

Placed on: | 13th February 2018 |

Closes: | 30th April 2018 |

**Programme of Research: **This programme of research is within the study of **finite group theory**. Group theory is the mathematical study of **symmetry** and has applications across the full range of mathematics.

Our particular focus will be on the symmetries of **relational structures** – these are mathematical objects that generalize the notion of a graph, or of a finite network. Any finite group can be thought of as the set of symmetries of a relational structure; indeed, for any given group, there may be many ways of doing this. A natural and important question is the following: given a particular group G how do we find a relational structure for which G is the set of symmetries, for which the structure is “as symmetric as possible”, and for which the structure “isn’t too complicated”? Answering this question for different families of groups has important implications in **model theory**, a branch of logic.

In the process of working on this project, the student can expect to learn a great deal about the structure of finite simple groups and, in particular, will study and make use of one of the most famous theorems in mathematics, the **Classification of Finite Simple Groups**.

Applicants should have a minimum of an upper second class honours degree in Mathematics and / or a good Masters’ degree.

The Studentship is to support full-time study for three years. Students will receive an annual tax-free bursary of £14,553 plus tuition fees paid at the Home / EU rate (currently £4,195 per annum).

Apply here: http://gro.southwales.ac.uk/next-step/

Please select MPhil/PhD (Computing/Maths) when applying. Applicants are not expected to submit a research proposal for this studentship.

Informal enquiries about the project can be made to Dr Nick Gill nick.gill@southwales.ac.uk

Closing date for applications is Monday 30^{th} April 2018 and the studentship will commence in October 2018.

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