Groups

• Finitely presented groups
  • Families of presentations represented by functions
  • Verifying correctness of a presentation for 3M(24)
  • Using low index subgroups to prove that a group is infinite
  • Proving that the Fibonacci group F(9) is infinite
  • Presentations for Burnside groups
  • Construction of maximal subgroups in a large finite group
• Permutation groups
  • Analysis of a small soluble permutation group
  • Shuffle groups
  • Action of PSL(3, 4) on flags
  • Construction of the design associated with
  • Normal structure of a primitive group
  • Subgroup lattice
• Matrix groups
  • Random generation of matrix group elements
  • The Molien series for a matrix group
• Soluble groups
  • Maximal subgroups of B(2,6)
  • Conjecture concerning size of a largest conjugacy class
  • A structural analysis on a polycyclic group

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