Generation of finite simple groups

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• Carlisle King, Imperial College
• Friday 12 February 2016, 15:00-16:00
• CMS, MR4.

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

Given a finite simple group G, it is natural to ask how many elements are needed to generate G. It has been shown that all finite simple groups are generated by a pair elements. A natural refinement is then to ask whether the orders of the generating elements may be restricted: given a pair of integers (a,b), does there exist a pair of elements (x,y) generating G with x of order a and y of order b? If such a pair exists, we say G is (a,b)-generated. I will explore some past results regarding (2,3)-generation as well as a new result on (2,p)-generation for some prime p.

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

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