Breadcrumb
Orbit-coherence in permutation groups
Wed 20 March 2013, 14:30
John Britnell
Imperial College London
Organisers: Tony Skyner, Neil Saunders
ABSTRACT
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). In this talk, I
shall talk about recent work with Mark Wildon (Royal Holloway), on the
subject of 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 S_n of any
element g is a lattice.