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Daniel Sykes, University of New England

Permutation Groups

Lecturers

Professor Michael Giudici, The University of Western Australia

Synopsis

Permutation groups embody the notion of a group being a measure of symmetry and are an important tool for exploring geometric and combinatorial structures. This course will look at the modern theory of permutation groups which takes advantage of recent advances in abstract group theory such as the Classification of Finite Simple Groups.

Course Overview

  • The course will cover topics such as group actions, wreath products, multiply transitive groups, primitive groups, the O’Nan-Scott Theorem, and will look at applications to study the symmetry of graphs such as Cayley graphs and 2-arc-transitive graphs.

Prerequisites

  • A first course in group theory that includes things such as groups, the symmetric and alternating groups, subgroups, cosets, normal subgroups, Lagrange’s Theorem, homomorphisms, isomorphisms and quotient groups.

Assessment

  • 3 weekly assignments worth 10% each. These will include marks for exposition of solutions, not just obtaining a correct one
  • In class problem solving. Students will be given two problems to work on in class under supervised conditions. 5% each
  • Final Exam held under exam conditions at home university 60%

(Assessment subject to change)

Resources/pre-reading (if available)

Lecture notes will be provided during the course.

Students who would like further reading on the topics should see the following books. Skeletal notes will also be provided during the course.

  • Permutation groups, by John D. Dixon and Brian Mortimer
  • Permutation groups, by Peter J. Cameron
  • Permutation groups and cartesian decompositions, by Cheryl E. Praeger and Csaba Schneider

Pre-Course Quiz

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Take this quiz and look at some of the expected foundational skills in this topic

michael-giudici

Professor Michael Giudici
The University of Western Australia

Michael Giudici completed his PhD at Queen Mary, University of London in 2002 under the supervision of Peter Cameron. He has been at UWA since then, where he held various positions until being promoted to Professor at the start of 2018. His research centres around permutation groups and their actions of combinatorial structures such as graphs.