### Permutations, bases and low rank groups

Algebra Seminar

19th March 2024, 4:00 pm – 5:00 pm

Fry Building, G.07

Let G = GL(V), where V is a finite-dimensional vector space, and recall that any element in G is uniquely determined by its action on a basis for V. In addition, any two pairs of linearly independent vectors can be mapped to each other by an element of G. These two basic linear algebra properties can be interpreted in the language of permutation groups, which leads us naturally to the definitions of base and rank of a permutation group. In this talk, I will present some of my recent results on bases for primitive permutation groups, and I will report on recent progress with C.H. Li and Y.Z. Zhu towards a classification of the rank three groups.

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