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Symmetric sets in NF
by
Thomas Forster
University of Cambridge
Coauthors: Nathan Bowler
A set is n-symmetric, if, thought of a an element of Pn(V), it is fixed by every permutation of V: that is to say, if its orbit under this n-th action of the symmetric group on V (its "n-orbit") is a singleton. A set is symmetric if it is n-symmetric for some n. It has been expected and desired that every set whose n-orbit is small is a indeed n-symmetric. We show that this is true if we consider instead n-symmetry-from-the-point-of-view-of-S, where S is the characteristic subgroup generated by permutations supported by a moiety (a set the size of the V whose complement is of size V). We show that every normal subgroup of Symm(V) of small index extends S and that S has no nontrivial normal subgroups of small index.
Date received: February 21, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caty-04.