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3/2-Generation

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GRA - Groups, representations and applications: new perspectives

Many interesting and surprising results have arisen from studying generating sets for groups, especially simple groups. For example, every finite simple group can be generated by just two elements. In fact, Guralnick and Kantor, in 2000, proved that in a finite simple group every nontrivial element is contained in a generating pair, a property known as 3/2-generation. This answers a 1962 question of Steinberg. In this talk I will report on recent progress towards classifying the finite 3/2-generated groups, and I will discuss joint work with Casey Donoven in which we found the first nontrivial examples of infinite 3/2-generated groups.




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