3/2-Generation of Finite Groups

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• Scott Harper, University of Bristol
• Friday 04 March 2016, 15:00-16:00
• CMS, 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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