Algebra seminar - Marina Anagnostopoulou-Merkouri
| Dates: | 25 March 2025 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Marina Anagnostopoulou-Merkouri |
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Title: The regularity number of a finite group
Abstract: Let $G$ be a transitive permutation group on a finite set $\Omega$ with point stabiliser $H$. Recall that a base for $G$ is a subset of $\Omega$ whose pointwise stabiliser in $G$ is trivial. The minimal size of a base is called the base size of $G$, denoted b(G), and this classical invariant has been widely studied for many years, finding many applications.
Observe that $b(G)$ coincides with the smallest positive integer $k$ such that $G$ has a regular orbit on the Cartesian product $(G/H)^k$. As a natural generalisation, we can consider the minimal number $r$ such that $G$ has a regular orbit on $(G/H_1) \times \cdots \times (G/H_r)$ for any core-free subgroups $H_1, \ldots, H_r$ of $G$. We call this invariant the regularity number of $G$.
In this talk, we will explain how a combination of probabilistic, combinatorial and computational methods can be used to study the regularity number of almost simple groups, as well as several other related problems. In particular, we will report on some recent progress towards extensions of well studied base size conjectures of Cameron and Vdovin. This is joint work with Tim Burness.
Speaker
Marina Anagnostopoulou-Merkouri
Organisation: University of Bristol
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
