Uniform Domination for Simple Groups

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• Scott Harper
• Wednesday 30 May 2018, 16:00-17:00
• Watson Building, Lecture Room A.

If you have a question about this talk, please contact Chris Parker.

It is well known that every finite simple group can be generated by just two elements. In fact, by a theorem of Guralnick and Kantor, there is a conjugacy class C such that for each non-identity element x there exists an element y in C such that x and y generate the entire group. Motivated by this, we introduce a new invariant for finite groups: the uniform domination number. This is the minimal size of a subset S of conjugate elements such that for each non-identity element x there exists an element s in S such that x and s generate the group. This invariant arises naturally in the study of generating graphs.

In this talk, I will present recent joint work with Tim Burness, which establishes best possible results on the uniform domination number for finite simple groups, using a mix of probabilistic and computational methods together with recent results on the base sizes of primitive permutation groups.

This talk is part of the Algebra Seminar series.

This talk is included in these lists:

• Algebra Seminar
• School of Mathematics Events
• Watson Building, Lecture Room A

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