Project description
Definable and pseudofinite groups
The EU-funded DEFGROUP project is exploring logic (model theory) and algebra (group theory), by studying groups known as 'first-order definable' in structures that satisfy certain model-theoretic restrictions. The project is working to show that groups definable in tame fields are closely related to the rational points of an algebraic group. The project is also working to prove that the soluble radical of any pseudofinite group with a simple theory is soluble. The project also aims to demonstrate that any infinite group definable in a pseudofinite field (or in any pseudofinite structure) is pseudofinite.
Objective
The proposed research links logic (model theory) and algebra (group theory). It explores groups which are first-order definable in structures that satisfy certain model-theoretic restrictions. The structures, here called `tame’, are stable, simple, NIP, or NTP2, concepts from Shelah's `generalised stability theory'. WP 1 concerns groups definable in tame fields, possibly equipped with extra operators. The aim is to show that a definable group in such fields must be closely related to the rational points of an algebraic group and to investigate the structure fixed pointwise by a generic automorphism in a generic differential difference field. WP 2 revolves around pseudofinite groups (infinite groups satisfying every sentence true of all finite groups), and gives a model theoretic perspective on finite group theory. One goal is to prove that the soluble radical of any pseudofinite group with a simple theory is soluble. Another is to solve the following question, possibly with a pseudofinite counterexample: given a `tame’ group G and a soluble subgroup H of G, is there a definable soluble subgroup of G containing H? The final WP2 objective concerns primitive pseudofinite permutation groups and in particular the question whether elementary extensions preserve primitivity. The two Workpackages are well-linked: for example, any infinite group definable in a pseudofinite field (or in any pseudofinite structure) is pseudofinite. The Fellow, Hempel, will receive training through research in Leeds, from the supervisor Macpherson and from the wider model theory group. She will benefit from the background of Macpherson on pseudofinite groups and permutation groups, and the broader experience of other Leeds model theorists. She will transfer to Leeds specific expertise on conditions such as NTP2, and on tame groups. She will receive training and opportunities complementary to her previous experience, on topics such as outreach, project management, and PhD student support.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics discrete mathematics mathematical logic
- natural sciences mathematics pure mathematics algebra
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) H2020-MSCA-IF-2018
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
LS2 9JT Leeds
United Kingdom
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.