Prime graphs, simple groups and Goldbach's conjecture.

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• Elisa Covato University of Bristol
• Friday 13 February 2015, 15:00-16:00
• CMS, MR14.

If you have a question about this talk, please contact Julian Brough.

Let G be a finite group. The prime graph of G is a graph with vertex set the set of primes dividing the order of G, and two vertices p and q are adjacent if and only if G contains an element of order pq. This notion has been studied extensively in recent years, with a particular focus on the prime graphs of simple groups. In this talk, I will determine all the pairs (G,H), where G is simple and H is a proper subgroup of G such that G and H have the same prime graph. Moreover, I will show that if G is the alternating group A_n and H is an intransitive subgroup, the problem of determining whether or not they have the same prime graph depends on some formidable open problems in number theory, such as Goldbach’s conjecture.

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

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