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SUMMARY:Prime graphs\, simple groups and Goldbach's conjecture. - Elisa Co
 vato University of Bristol
DTSTART:20150213T150000Z
DTEND:20150213T160000Z
UID:TALK58051@talks.cam.ac.uk
CONTACT:Julian Brough
DESCRIPTION: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 vert
 ices p and q are adjacent if and only if G contains an element of or
 der 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 pr
 oper subgroup of G such that G and H have the same prime graph. More
 over\, I will show that if G is the alternating group A_n and H is a
 n intransitive subgroup\, the problem of determining whether or not they 
 have the same prime graph depends on some formidable open problems in numb
 er theory\, such as Goldbach's conjecture.
LOCATION:CMS\, MR14
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