Orbit-coherence in permutation groups

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• John Britnell, Imperial College
• Wednesday 04 June 2014, 16:30-17:30
• MR12.

If you have a question about this talk, please contact David Stewart.

For a permutation g of a set X, let p(g) be the partition of X given by the orbits of g. For a permutation group G on X, let p(G) be the set of partitions p(g) for g in G. The set of all partitions of X forms a complete lattice under the refinement order, and it makes sense to look at the order-theoretic properties of the subset p(G).

I shall talk about joint work with Mark Wildon (Royal Holloway), on permutation groups G for which p(G) is an upper- or lower-semilattice. In either case, this is a highly restrictive condition on G, but there are many interesting examples, in both finite and infinite degree. In particular, the centralizer in Sym(X) of an element g is always a lower-semilattice, and, subject to a finiteness condition on the cycles of g, a lattice.

This talk is part of the Algebra and Representation Theory Seminar series.

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