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New properties of permutation groups

Marina Anagnostopoulou-Merkouri

University of Bristol

Time: 16:00-17:00 (GMT+8), Tuesday October 24th, 2023
Location: Zoom

Abstract: Primitivity and quasiprimitivity are very important and widely studied properties of permutation groups. It is easy to show that every primitive group is quasiprimitive, but the converse doesn't always hold. Both those properties go back to Galois and it is argued that he in fact got confused between the two. In this talk we will discuss a new property that we call pre-primitivity that is designed so that a transitive group $G$ is primitive if and only if it is quasiprimitive and pre-primitive. We will also discuss other newly defined properties of permutation groups related to the combinatorial properties of their invariant partition lattices, and see how those properties relate to each other.

Host: 黄弘毅 Hong Yi Huang

Slides