Please join us for the following up-coming Virtual Combinatorics
Colloquium. The zoom link is below, and a poster can be found here
https://sites.google.com/view/northeastcombinatoricsnetwork/virtual-combinatorics-colloquium.
Past VCC presentations, which may also be of interest for online courses,
may be found here:
https://sites.google.com/view/northeastcombinatoricsnetwork/virtual-combinatorics-colloquium/past-vccs
Please share this information.
Speaker: Cheryl Praeger (University of Western Australia),
Title: "Diagonal Structures and Permutation Groups".
Date and Time: Tuesday June 30, 2020, 9:00am EDT (13:00 UTC)
Zoom Meeting ID: 913 6952 1801 (active link below)
Password: 16180339
Abstract. Permutation groups are often best understood by the
structures they preserve on the underlying point set. For example, several
families of maximal subgroups of finite symmetric groups arise as
stabilisers of subsets, or partitions, or Cartesian decompositions of the
point set. Among the finite primitive groups, one family (apart from the
almost simple groups) resisted such a description until now, namely the
maximal simple diagonal groups. We introduce the concept of a diagonal
structure associated with any group T, finite or infinite, and any integer
m at least 2. We prove that the stabiliser of the diagonal structure is
precisely the corresponding diagonal group, and that this group is
primitive essentially when T is characteristically simple.
This work began as a collaboration with Csaba Schneider, and over the past
almost two years the collaboration includes also R. A. Bailey and Peter
Cameron. We have introduced also a diagonal graph, built from a collection
of Hamming graphs: its automorphism group is the diagonal group. And there
are close connections with Latin squares, and with certain kinds of higher
dimensional Latin hypercubes. We continue to learn more about the
combinatorial links.
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Meeting ID: 913 6952 1801
Password: 16180339
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*Jo*
Jo Ellis-Monaghan
Chair, Department of Mathematics and Statistics (on sabbatical 2019-2020)
Editor-in-Chief, PRIMUS
Saint Michael's College
One Winooski Park
Colchester, VT 05439
office: Jeanmarie 279
website: http://academics.smcvt.edu/jellis-monaghan/
phone: 802 654 2660
fax: 802 654 2960
e-mail: je <jellis-monaghan@smcvt.edu>llismonaghan@gmail.com
<llismonaghan@gmail.com>
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