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3/2-Generation of Finite Groups

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  • UserScott Harper, University of Bristol
  • ClockFriday 04 March 2016, 15:00-16:00
  • HouseCMS, MR4.

If you have a question about this talk, please contact Nicolas Dupré .

It is well known that every finite simple group can be generated by two elements. Moreover, two arbitrary elements are very likely to generate the whole group. For example, every non-identity element of a finite simple group belongs to a generating pair. Groups with the latter property are said to be 3/2-generated. It is natural to ask which other finite groups are 3/2-generated. In 2008, Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient of the group is cyclic. In this talk we will discuss recent progress towards establishing this conjecture, where probabilistic techniques play a key role. We will also discuss some related open problems.

This talk is part of the Junior Algebra and Number Theory seminar series.

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